-
1
-
-
0003851729
-
-
National Bureau of Standards, Washington, DC
-
M. ABRAMOWITZ, I. A. STEGUN, Editors (1972). Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables. National Bureau of Standards, Washington, DC. 1046 pp.
-
(1972)
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables
, pp. 1046
-
-
Abramowitz, M.1
Stegun, I.A.2
-
5
-
-
0003689132
-
-
Academic Press, New York, NY
-
R. B. ASH (1972). Measure, Integration, and Functional Analysis. Academic Press, New York, NY. 284 pp.
-
(1972)
Measure, Integration, and Functional Analysis
, pp. 284
-
-
Ash, R.B.1
-
6
-
-
84868023539
-
On thew discrepancy of the Halton sequence
-
E. I. ATANASSOV (2002). On thew discrepancy of the Halton sequence. Mathematica Balkanica, New Series, Vol. 20, pp. 1-18.
-
(2002)
Mathematica Balkanica, New Series
, vol.20
, pp. 1-18
-
-
Atanassov, E.I.1
-
10
-
-
0004302610
-
-
John Wiley & Sons, New York, NY Second Edition
-
P. BILLINGSLEY (1986). Probability and Measure. John Wiley & Sons, New York, NY (Second Edition). 622 pp.
-
(1986)
Probability and Measure
, pp. 622
-
-
Billingsley, P.1
-
11
-
-
0001560259
-
Countable probabilities and their applications in arithmetic
-
E. BOREL (1909). Countable probabilities and their applications in arithmetic. Rend. Circ. Mat. Palermo, Vol. 27, pp. 247-271.
-
(1909)
Rend. Circ. Mat. Palermo
, vol.27
, pp. 247-271
-
-
Borel, E.1
-
12
-
-
0003449873
-
-
Albin Michel, Paris, Prentice-Hall, Englewood Cliffs, NJ English Edition, 1965
-
E. BOREL (1965). Elements of the Theory of Probability. Albin Michel, Paris (1950); Prentice-Hall, Englewood Cliffs, NJ (English Edition, 1965). 179 pp.
-
(1950)
Elements of the Theory of Probability
, pp. 179
-
-
Borel, E.1
-
14
-
-
0003959736
-
-
Hermann, Paris, France, and Addison-Wesley, Reading, MA
-
N. BOURBAKI (1966). Elements of Mathematics: General Topology. Part I. Hermann, Paris, France, and Addison-Wesley, Reading, MA. 437 pp.
-
(1966)
Elements of Mathematics: General Topology. Part I
, pp. 437
-
-
Bourbaki, N.1
-
15
-
-
0004256573
-
-
Addison-Wesley, Reading, MA
-
L. BREIMAN (1968). Probability. Addison-Wesley, Reading, MA. 421 pp.
-
(1968)
Probability
, pp. 421
-
-
Breiman, L.1
-
16
-
-
0004167528
-
-
Verlag Harri Deutsch, Thun, Switzerland, and Frankfurt/Main, Germany
-
I. N. BRONSHTEIN, K. A. SEMENDYAYEV (1985). Handbook of Mathematics. Verlag Harri Deutsch, Thun, Switzerland, and Frankfurt/Main, Germany. 973 pp.
-
(1985)
Handbook of Mathematics
, pp. 973
-
-
Bronshtein, I.N.1
Semendyayev, K.A.2
-
17
-
-
0039719333
-
-
Yu. A. Shreider; Fizmatgiz, Moscow, USSR; Elsevier, Amsterdam, Netherlands 1964
-
N. P. BUSLENKO, D. I. GOLENKO, YU. A. SHREIDER, I. M. SOBOL', V. G. SRAGOVICH (1966). The Method of Statistical Trials-The Monte Carlo Method. Edited by Yu. A. Shreider; Fizmatgiz, Moscow, USSR (1962); Elsevier, Amsterdam, Netherlands (1964), 312 pp.;
-
(1962)
The Method of Statistical Trials-The Monte Carlo Method
, pp. 312
-
-
Buslenko, N.P.1
Golenko, D.I.2
Shreider, Yu.A.3
Sobol, I.M.4
Sragovich, V.G.5
-
18
-
-
84868014674
-
On probability as the limit of frequency
-
F. P. CANTELLI (1917). On probability as the limit of frequency. Rend. Acad. Lincei, Vol. 26, p. 39.
-
(1917)
Rend. Acad. Lincei
, vol.26
, pp. 39
-
-
Cantelli, F.P.1
-
19
-
-
0003535774
-
-
Academic Press, New York, NY
-
G. CHOQUET (1966). Topology. Academic Press, New York, NY. 337 pp.
-
(1966)
Topology
, pp. 337
-
-
Choquet, G.1
-
21
-
-
0004254001
-
-
Cambridge University Press, Cambridge, England
-
E. T. COPSON (1968). Metric Spaces. Cambridge University Press, Cambridge, England. 143 pp.
-
(1968)
Metric Spaces
, pp. 143
-
-
Copson, E.T.1
-
24
-
-
0000272653
-
Randomization of number theoretic methods for multiple integration
-
R. CRANLEY, T. N. L. PATTERSON (1976). Randomization of number theoretic methods for multiple integration. SIAM J. Numer. Anal., Vol. 13, pp. 904-914.
-
(1976)
SIAM J. Numer. Anal.
, vol.13
, pp. 904-914
-
-
Cranley, R.1
Patterson, T.N.L.2
-
25
-
-
0041707044
-
Asymptotic complexity of Monte Carlo methods for solving linear systems
-
D. L. DANILOV, S. M. ERMAKOV, J. H. HALTON (2000). Asymptotic complexity of Monte Carlo methods for solving linear systems. J. Stat. Planning & Inference, Vol. 85, pp. 5-18.
-
(2000)
J. Stat. Planning & Inference
, vol.85
, pp. 5-18
-
-
Danilov, D.L.1
Ermakov, S.M.2
Halton, J.H.3
-
27
-
-
4544355067
-
-
Cambridge University Press, Cambridge, England
-
R. M. DUDLEY (2002). Real Analysis and Probability. Cambridge University Press, Cambridge, England. 555 pp.
-
(2002)
Real Analysis and Probability
, pp. 555
-
-
Dudley, R.M.1
-
28
-
-
0003535772
-
-
Allyn & Bacon, Boston, MA
-
J. DUGUNDJI (1966). Topology. Allyn & Bacon, Boston, MA. 447 pp.
-
(1966)
Topology
, pp. 447
-
-
Dugundji, J.1
-
31
-
-
0004118552
-
-
Holt, Rinehart & Winston, NY
-
M. EISENBERG (1974). Topology. Holt, Rinehart & Winston, NY. 427 pp.
-
(1974)
Topology
, pp. 427
-
-
Eisenberg, M.1
-
32
-
-
27644505429
-
Quasi-Monte Carlo methods for numerical integration of multivariate Haar series
-
K. ENTACHER (1997). Quasi-Monte-Carlo methods for numerical integration of multivariate Haar series. BIT, Vol. 31, pp. 846-861. (Pubitemid 127725541)
-
(1997)
BIT Numerical Mathematics
, vol.37
, Issue.4
, pp. 846-861
-
-
Entacher, K.1
-
35
-
-
0001013260
-
The discrepancy of sequences associated with a system of numbering (in s dimensions)
-
H. FAURE (1982). The discrepancy of sequences associated with a system of numbering (in s dimensions). Acta Arith., Vol. 41, pp. 337-351.
-
(1982)
Acta Arith.
, vol.41
, pp. 337-351
-
-
Faure, H.1
-
36
-
-
24144443925
-
Study of discrepancies of generalized van der Corput sequences
-
H. FAURE (1983). Study of discrepancies of generalized van der Corput sequences. J. Number Theory, Vol. 16, pp. 376-394.
-
(1983)
J. Number Theory
, vol.16
, pp. 376-394
-
-
Faure, H.1
-
39
-
-
0038144725
-
Deterministic simulation of random processes
-
J. N. FRANKLIN (1963). Deterministic simulation of random processes. Math. Comp., Vol. 17, pp. 28-59.
-
(1963)
Math. Comp.
, vol.17
, pp. 28-59
-
-
Franklin, J.N.1
-
43
-
-
0004147936
-
-
Marcel Dekker, New York, NY Second Edition
-
J. GALAMBOS (1995). Advanced Probability Theory. Marcel Dekker, New York, NY (Second Edition). 461 pp.
-
(1995)
Advanced Probability Theory
, pp. 461
-
-
Galambos, J.1
-
44
-
-
0001869773
-
On the empirical determination of probability laws
-
V. I. GLIVENKO (1933). On the empirical determination of probability laws. Giorn. Ist. Ital. Attuari, Vol. 4, p. 92.
-
(1933)
Giorn. Ist. Ital. Attuari
, vol.4
, pp. 92
-
-
Glivenko, V.I.1
-
45
-
-
0004134071
-
-
Chelsea, New York, NY Second Edition
-
B. V. GNEDENKO (1963). The Theory of Probability. Chelsea, New York, NY (Second Edition). 471 pp.
-
(1963)
The Theory of Probability
, pp. 471
-
-
Gnedenko, B.V.1
-
48
-
-
0003498504
-
-
Academic Press, New York, NY
-
I. S. GRADSHTEYN, I. M. RYZHIK (1965). Table of Integrals, Series, and Products. Academic Press, New York, NY. 1086 pp.
-
(1965)
Table of Integrals, Series, and Products
, pp. 1086
-
-
Gradshteyn, I.S.1
Ryzhik, I.M.2
-
49
-
-
0004207439
-
-
Springer-Verlag, New York. NY
-
P. R. HALMOS (1950). Measure Theory. Springer-Verlag, New York. NY. 304 pp.
-
(1950)
Measure Theory
, pp. 304
-
-
Halmos, P.R.1
-
50
-
-
0002020770
-
On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals
-
J. H. HALTON (1960). On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numer. Math., Vol. 2, pp. 84-90.
-
(1960)
Numer. Math.
, vol.2
, pp. 84-90
-
-
Halton, J.H.1
-
53
-
-
84868034765
-
On the relative merits of correlated and importance sampling for Monte Carlo integration
-
J. H. HALTON (1965a). On the relative merits of correlated and importance sampling for Monte Carlo integration. Proc. Cambridge Philos. Soc., Vol. 61, pp. 497-498.
-
(1965)
Proc. Cambridge Philos. Soc.
, vol.61
, pp. 497-498
-
-
Halton, J.H.1
-
57
-
-
0039060092
-
The distribution of the sequence {nx} (n = 0, 1, 2,...)
-
J. H. HALTON (1965e). The distribution of the sequence {nx} (n = 0, 1, 2,...) Proc. Cambridge Philos. Soc., Vol. 61, pp. 665-670.
-
(1965)
Proc. Cambridge Philos. Soc.
, vol.61
, pp. 665-670
-
-
Halton, J.H.1
-
58
-
-
84868028091
-
-
Univ. Wisconsin, Madison, Math. Res. Ctr., Tech. Rep
-
J. H. HALTON (1966a). On the strong convergence of linear averages. Univ. Wisconsin, Madison, Math. Res. Ctr., Tech. Rep. No. 719, 8 pp.
-
(1966)
On the Strong Convergence of Linear Averages
, Issue.719
, pp. 8
-
-
Halton, J.H.1
-
59
-
-
0342729979
-
An interpretation of negative probabilities
-
J. H. HALTON (1966b). An interpretation of negative probabilities. Proc. Cambridge Philos. Soc., Vol. 62, pp. 83-86.
-
(1966)
Proc. Cambridge Philos. Soc.
, vol.62
, pp. 83-86
-
-
Halton, J.H.1
-
60
-
-
84868006592
-
-
Univ. Wisconsin, Madison, Math. Res. Ctr., Tech. Rep
-
J. H. HALTON (1967). Sequential Monte Carlo (Revised). Univ. Wisconsin, Madison, Math. Res. Ctr., Tech. Rep. No. 816, 38 pp.
-
(1967)
Sequential Monte Carlo (Revised)
, Issue.816
, pp. 38
-
-
Halton, J.H.1
-
61
-
-
0014705837
-
A retrospective and prospective survey of the Monte Carlo method
-
J. H. HALTON (1970). A retrospective and prospective survey of the Monte Carlo method. SIAM Review, Vol. 12, pp. 1-63.
-
(1970)
SIAM Review
, vol.12
, pp. 1-63
-
-
Halton, J.H.1
-
62
-
-
84868022901
-
Estimating the accuracy of quasi-Monte-Carlo calculations
-
S. K. Zaremba; Academic Press, New York, NY, 1972
-
J. H. HALTON (1972). Estimating the accuracy of quasi-Monte-Carlo calculations. Applications of Number Theory to Numerical Analysis (Editor, S. K. Zaremba; Academic Press, New York, NY, 1972) pp. 345-360.
-
(1972)
Applications of Number Theory to Numerical Analysis
, pp. 345-360
-
-
Halton, J.H.1
-
63
-
-
85039692081
-
-
Univ. Wisconsin, Madison, CS Dept., Tech. Rep
-
J. H. HALTON (1979). An explicit formulation of the generalized antithetic transformation for Monte Carlo integration. Univ. Wisconsin, Madison, CS Dept., Tech. Rep. No. 348, 5 pp.
-
(1979)
An Explicit Formulation of the Generalized Antithetic Transformation for Monte Carlo Integration
, Issue.348
, pp. 5
-
-
Halton, J.H.1
-
64
-
-
84889266837
-
-
Univ. Wisconsin, Madison, CS Dept., Tech. Rep
-
J. H. HALTON (1980). Generalized antithetic transformations for Monte Carlo sampling. Univ. Wisconsin, Madison, CS Dept., Tech. Rep. No. 408, 39 pp.
-
(1980)
Generalized Antithetic Transformations for Monte Carlo Sampling
, Issue.408
, pp. 39
-
-
Halton, J.H.1
-
65
-
-
84868006606
-
-
Univ. North Carolina, Chapel Hill, CS Dept., Tech. Rep. No. 88-003
-
J. H. HALTON (1988a). Tree-structured pseudo-random sequences. Univ. North Carolina, Chapel Hill, CS Dept., Tech. Rep. No. 88-003, 84 pp.
-
(1988)
Tree-structured Pseudo-random Sequences
, pp. 84
-
-
Halton, J.H.1
-
66
-
-
0023995659
-
On the efficiency of generalized antithetic transformations for Monte Carlo integration
-
J. H. HALTON (1988b). On the efficiency of generalized antithetic transformations for Monte Carlo integration. Nucl. Sci. and Eng., Vol. 98, pp. 299-316.
-
(1988)
Nucl. Sci. and Eng.
, vol.98
, pp. 299-316
-
-
Halton, J.H.1
-
67
-
-
84868015218
-
-
Univ. North Carolina, Chapel Hill, CS Dept., Tech. Rep. No. 88-034
-
J. H. HALTON (1988c). On the random covering problem. Univ. North Carolina, Chapel Hill, CS Dept., Tech. Rep. No. 88-034, 31 pp.
-
(1988)
On the Random Covering Problem
, pp. 31
-
-
Halton, J.H.1
-
68
-
-
38249026363
-
Pseudo-random trees-multiple independent sequence generators for parallel and branching computations
-
J. H. HALTON (1989). Pseudo-random trees-multiple independent sequence generators for parallel and branching computations. J. Comput. Phys., Vol. 84, pp. 1-56.
-
(1989)
J. Comput. Phys.
, vol.84
, pp. 1-56
-
-
Halton, J.H.1
-
71
-
-
34249915776
-
Random sequences in Fréchet spaces
-
J. H. HALTON (1991a). Random sequences in Fréchet spaces. J. Sci. Comp., Vol. 6, pp. 61-77.
-
(1991)
J. Sci. Comp.
, vol.6
, pp. 61-77
-
-
Halton, J.H.1
-
72
-
-
0026383268
-
Random sequences in generalized Cantor sets
-
J. H. HALTON (1991b). Random sequences in generalized Cantor sets. J. Sci. Comp., Vol. 6, pp. 415-423.
-
(1991)
J. Sci. Comp.
, vol.6
, pp. 415-423
-
-
Halton, J.H.1
-
73
-
-
85039682096
-
The Monte Carlo solution of linear systems
-
Chapel Hill, CS Dept., Working Paper
-
J. H. HALTON (1991c). The Monte Carlo solution of linear systems. Univ. North Carolina, Chapel Hill, CS Dept., Working Paper, 132 pp.
-
(1991)
Univ. North Carolina
, pp. 132
-
-
Halton, J.H.1
-
74
-
-
84858412096
-
An introduction to the Monte Carlo solution of linear systems
-
Brussels, Belgium, April 1991
-
J. H. HALTON (1991d). "An introduction to the Monte Carlo solution of linear systems." Invited presentation at IMACS International Symposium on Iterative Methods in Linear Algebra, Brussels, Belgium, April 1991. 18 pp.
-
(1991)
IMACS International Symposium on Iterative Methods in Linear Algebra
, pp. 18
-
-
Halton, J.H.1
-
75
-
-
0041541977
-
Some new results on the Monte Carlo solution of linear systems, including sequential methods
-
Brussels, Belgium, April 1991
-
J. H. HALTON (1991e). "Some new results on the Monte Carlo solution of linear systems, including sequential methods." Invited presentation at IMACS International Symposium on Iterative Methods in Linear Algebra, Brussels, Belgium, April 1991. 20 pp.
-
(1991)
IMACS International Symposium on Iterative Methods in Linear Algebra
, pp. 20
-
-
Halton, J.H.1
-
76
-
-
34249843351
-
Reject the rejection technique
-
1992
-
J. H. HALTON (1992). Reject the rejection technique. J. Sci. Comp., Vol. 7 (1992) pp. 281-287.
-
(1992)
J. Sci. Comp.
, vol.7
, pp. 281-287
-
-
Halton, J.H.1
-
77
-
-
0028458133
-
Sequential Monte Carlo techniques for the solution of linear systems
-
J. H. HALTON (1994). Sequential Monte Carlo techniques for the solution of linear systems. J. Sci. Comp., Vol. 9, pp. 213-257.
-
(1994)
J. Sci. Comp.
, vol.9
, pp. 213-257
-
-
Halton, J.H.1
-
79
-
-
84868009054
-
Sequential Monte Carlo techniques for solving non-linear systems
-
Los Alamos, New Mexico, August 1996
-
J. H. HALTON (1996b). "Sequential Monte Carlo techniques for solving non-linear systems." Invited presentation at CNLS/LANL Workshop on Adaptive Monte Carlo Methods, Los Alamos, New Mexico, August 1996. 35 pp.
-
(1996)
CNLS/LANL Workshop on Adaptive Monte Carlo Methods
, pp. 35
-
-
Halton, J.H.1
-
80
-
-
84868006608
-
A rigorous justification for quasi-Monte-Carlo methods and valid statistical estimates of their accuracy
-
Stennis Space Center, 22-24 April 1998
-
J. H. HALTON (1998a). "A rigorous justification for quasi-Monte-Carlo methods and valid statistical estimates of their accuracy." Invited presentation at Monte Carlo workshop, Stennis Space Center, 22-24 April 1998.
-
(1998)
Monte Carlo Workshop
-
-
Halton, J.H.1
-
81
-
-
84868023468
-
Independence of quasi-random sequences and sets
-
Claremont Graduate School, Claremont, CA 1998
-
J. H. HALTON (1998b). "Independence of quasi-random sequences and sets." Invited presentation at International Conference on Monte Carlo and Quasi-Monte-Carlo Methods, Claremont Graduate School, Claremont, CA, 1998.
-
(1998)
International Conference on Monte Carlo and Quasi-Monte-Carlo Methods
-
-
Halton, J.H.1
-
83
-
-
84868023471
-
Sequential Monte Carlo techniques for solving nonlinear problems
-
Universitat di Girona, Girona, Spain, 25 May 2001-9 June 2001
-
J. H. HALTON (2001a). "Sequential Monte Carlo techniques for solving nonlinear problems." Public lecture (Lluis Santalo Lecture on Applied Mathematics), during invited visit to Universitat di Girona, Girona, Spain, 25 May 2001-9 June 2001.
-
(2001)
Public Lecture (Lluis Santalo Lecture on Applied Mathematics)
-
-
Halton, J.H.1
-
86
-
-
85039673911
-
Quasi-probability: Invited opening plenary lecture
-
15-19 September 2003, Berlin, Germany, sponsored by Weierstrass Institute of Applied Analysis, Konrad Zuse Center for Scientific Computing, and Humboldt University
-
J. H. HALTON (2003a). Quasi-probability: Invited opening plenary lecture, 4th IMACS Seminar on Monte Carlo Methods, 15-19 September 2003, Berlin, Germany (sponsored by Weierstrass Institute of Applied Analysis, Konrad Zuse Center for Scientific Computing, and Humboldt University).
-
(2003)
4th IMACS Seminar on Monte Carlo Methods
-
-
Halton, J.H.1
-
87
-
-
84868028095
-
A new approach to the rigorous validation of quasi-Monte-Carlo methods
-
2003
-
J. H. HALTON (2003b). "A new approach to the rigorous validation of quasi-Monte-Carlo methods." Proc. 7th JCIS, 2003. p. 1758.
-
(2003)
Proc. 7th JCIS
, pp. 1758
-
-
Halton, J.H.1
-
88
-
-
84858379872
-
An outline of quasi-probability-why quasi-Monte-Carlo methods are statistically valid and how their errors can be estimated statistically
-
J. H. HALTON (2004). An outline of quasi-probability-why quasi-Monte-Carlo methods are statistically valid and how their errors can be estimated statistically. Monte Carlo Methods & Appl., Vol. 10, pp. 183-196.
-
(2004)
Monte Carlo Methods & Appl.
, vol.10
, pp. 183-196
-
-
Halton, J.H.1
-
89
-
-
84868029266
-
Sequential Monte Carlo techniques for solving non-linear systems
-
Florida State University, Tallahassee, FL, May 2005
-
J. H. HALTON (2005). "Sequential Monte Carlo techniques for solving non-linear systems." Invited presentation at Fifth IMACS Seminar on Monte Carlo Methods-MCM2005, Florida State University, Tallahassee, FL, May 2005. 26 pp.
-
(2005)
Fifth IMACS Seminar on Monte Carlo Methods-MCM2005
, pp. 26
-
-
Halton, J.H.1
-
90
-
-
0038483473
-
A method for increasing the efficiency of Monte Carlo integration
-
J. H. HALTON, D. C. HANDSCOMB (1957). A method for increasing the efficiency of Monte Carlo integration. J. ACM, Vol. 4, pp. 329-340
-
(1957)
J. ACM
, vol.4
, pp. 329-340
-
-
Halton, J.H.1
Handscomb, D.C.2
-
91
-
-
85039677330
-
Increasing the efficiency of radiation shielding calculations by using antithetic variates
-
Brussels, Belgium, April
-
J. H. HALTON, P. K. SARKAR (1998). Increasing the efficiency of radiation shielding calculations by using antithetic variates. Invited presentation at IMACS Seminar on Monte Carlo Methods, Université Libre de Bruxelles, Brussels, Belgium, April 1997, 35 pp.;
-
(1997)
IMACS Seminar on Monte Carlo Methods, Université Libre de Bruxelles
, pp. 35
-
-
Halton, J.H.1
Sarkar, P.K.2
-
92
-
-
85039690594
-
-
Simulation
-
Math. & Comp. in Simulation, VOL. 47, PP. 309-318.
-
Math. & Comp.
, vol.47
, pp. 309-318
-
-
-
93
-
-
84945708500
-
Algorithm 247: Radical-inverse quasi-random point sequence [G5]
-
J. H. HALTON, G. B. SMITH (1964). Algorithm 247: radical-inverse quasi-random point sequence [G5]. Comm. ACM, Vol. 7, pp. 701-702.
-
(1964)
Comm. ACM
, vol.7
, pp. 701-702
-
-
Halton, J.H.1
Smith, G.B.2
-
94
-
-
0000835150
-
The extreme and L discrepancies of some plane sets
-
J. H. HALTON, S. K. ZAREMBA (1969). The extreme and L discrepancies of some plane sets. Monatsh. Math., Vol. 73, pp. 316-328.
-
(1969)
Monatsh. Math.
, vol.73
, pp. 316-328
-
-
Halton, J.H.1
Zaremba, S.K.2
-
95
-
-
0345906513
-
-
Univ. Wisconsin, Madison, CS Dept., Tech. Rep
-
J. H. HALTON, E. A. ZEIDMAN (1969). Monte Carlo integration with sequential stratification. Univ. Wisconsin, Madison, CS Dept., Tech. Rep. No. 61, 31 pp.
-
(1969)
Monte Carlo Integration with Sequential Stratification
, Issue.61
, pp. 31
-
-
Halton, J.H.1
Zeidman, E.A.2
-
96
-
-
0346537591
-
-
Univ. Wisconsin, Madison, CS Dept., Tech. Rep
-
J. H. HALTON, E. A. ZEIDMAN (1971). The evaluation of multidimensional integrals by the Monte Carlo sequential stratification technique. Univ. Wisconsin, Madison, CS Dept., Tech. Rep. No. 137, 158 pp.
-
(1971)
The Evaluation of Multidimensional Integrals by the Monte Carlo Sequential Stratification Technique
, Issue.137
, pp. 158
-
-
Halton, J.H.1
Zeidman, E.A.2
-
97
-
-
84893792941
-
Monte Carlo methods for solving multivariable problems
-
J. M. HAMMERSLEY (1960). Monte Carlo methods for solving multivariable problems. Ann. N. Y. Acad. Sci., Vol. 86, pp. 844-874.
-
(1960)
Ann. N. Y. Acad. Sci.
, vol.86
, pp. 844-874
-
-
Hammersley, J.M.1
-
98
-
-
0003531332
-
-
Methuen, London, England; John Wiley & Sons, New York, NY
-
J. M. HAMMERSLEY, D. C. HANDSCOMB (1964). Monte Carlo Methods. Methuen, London, England; John Wiley & Sons, New York, NY. 185 pp.
-
(1964)
Monte Carlo Methods
, pp. 185
-
-
Hammersley, J.M.1
Handscomb, D.C.2
-
99
-
-
0004282089
-
-
Addison-Wesley, Reading, MA
-
B. HARRIS (1966). Theory of Probability. Addison-Wesley, Reading, MA. 294 pp.
-
(1966)
Theory of Probability
, pp. 294
-
-
Harris, B.1
-
100
-
-
0030259017
-
The mean square discrepancy of randomized nets
-
F. J. HICKERNELL (1996). The mean square discrepancy of randomized nets. ACM Trans. Modeling & Computer Simul., Vol. 6, pp. 274-296.
-
(1996)
ACM Trans. Modeling & Computer Simul.
, vol.6
, pp. 274-296
-
-
Hickernell, F.J.1
-
101
-
-
0034432296
-
The mean square discrepancy of scrambled (t, s)-sequences
-
DOI 10.1137/S0036142999358019, PII S0036142999358019
-
F. J. HICKERNELL, R. X. YUE (2001). The mean square discrepancy of scrambled (t, s)-sequences. SIAM J. Numer. Anal., Vol. 38, pp. 1089-1112. (Pubitemid 33645544)
-
(2001)
SIAM Journal on Numerical Analysis
, vol.38
, Issue.4
, pp. 1089-1112
-
-
Hickernell, F.J.1
Yue, R.-X.2
-
102
-
-
84868008288
-
Functions of bounded variation in the theory of uniform distribution
-
E. HLAWKA (1961). Functions of bounded variation in the theory of uniform distribution. Ann. Mat. Pura Appl., Vol. IV: 54, pp. 325-334.
-
(1961)
Ann. Mat. Pura Appl.
, vol.4
, Issue.54
, pp. 325-334
-
-
Hlawka, E.1
-
103
-
-
0003604023
-
-
Cambridge University Press, Cambridge, England Third Edition, 1927, Reprinted by Dover Publications
-
E. W. HOBSON (1927). The Theory of Functions of a Real Variable and the Theory of Fourier's Series. Volume 1. Cambridge University Press, Cambridge, England (Third Edition, 1927). Reprinted by Dover Publications (1957). 732 pp.
-
(1927)
The Theory of Functions of a Real Variable and the Theory of Fourier's Series
, vol.1
, pp. 732
-
-
Hobson, E.W.1
-
104
-
-
0003543263
-
-
Science Press, Beijing, PRC; Springer-Verlag, Berlin, Germany 1981
-
L. K. HUA, Y. WANG (1981). Applications of Number Theory to Numerical Analysis. Science Press, Beijing, PRC (1978); Springer-Verlag, Berlin, Germany (1981). 241 pp.
-
(1978)
Applications of Number Theory to Numerical Analysis
, pp. 241
-
-
Hua, L.K.1
Wang, Y.2
-
110
-
-
0002745071
-
A general theorem from the theory of distribution modulo 1
-
J. F. KOKSMA (1942). A general theorem from the theory of distribution modulo 1. Mathematika Zutphen, Vol. B11, pp. 7-11.
-
(1942)
Mathematika Zutphen
, vol.B11
, pp. 7-11
-
-
Koksma, J.F.1
-
111
-
-
0040367813
-
On sums of independent random variables
-
A. N. KOLMOGOROV (1928). On sums of independent random variables. Math. Ann., Vol. 99, pp. 309-319.
-
(1928)
Math. Ann.
, vol.99
, pp. 309-319
-
-
Kolmogorov, A.N.1
-
112
-
-
0013002691
-
On the strong law of large numbers
-
A. N. KOLMOGOROV (1930). On the strong law of large numbers. C. R. Acad. Sci. Paris, vol. 191, pp. 910-912.
-
(1930)
C. R. Acad. Sci. Paris
, vol.191
, pp. 910-912
-
-
Kolmogorov, A.N.1
-
113
-
-
0000189685
-
On the analytic method in probability theory
-
A. N. KOLMOGOROV (1931). On the analytic method in probability theory. Math. Ann., Vol. 104, pp. 415-458.
-
(1931)
Math. Ann.
, vol.104
, pp. 415-458
-
-
Kolmogorov, A.N.1
-
114
-
-
84858386368
-
-
Berlin, Chelsea, New York, NY Second English Edition, 1956
-
A. N. KOLMOGOROV (1956). Foundations of the Theory of Probability. Berlin (1933); Chelsea, New York, NY (Second English Edition, 1956). 84 pp.
-
(1933)
Foundations of the Theory of Probability
, pp. 84
-
-
Kolmogorov, A.N.1
-
115
-
-
0002135179
-
-
Addison-Wesley, Reading, MA
-
K. KRICKEBERG (1965). Probability Theory. Addison-Wesley, Reading, MA. 230 pp.
-
(1965)
Probability Theory
, pp. 230
-
-
Krickeberg, K.1
-
117
-
-
0007260337
-
-
Pergamon Press, Oxford, England, and Addison-Wesley, Reading, MA
-
K. KURATOWSKI (1961). Introduction to Set Theory and Topology. Pergamon Press, Oxford, England, and Addison-Wesley, Reading, MA. 283 pp.
-
(1961)
Introduction to Set Theory and Topology
, pp. 283
-
-
Kuratowski, K.1
-
118
-
-
84950845039
-
On the determination of probability laws through their characteristic functions
-
P. LÉVY (1922). On the determination of probability laws through their characteristic functions. C. R. Acad. Sci. Paris, Vol. 165, pp. 854-856.
-
(1922)
C. R. Acad. Sci. Paris
, vol.165
, pp. 854-856
-
-
Lévy, P.1
-
119
-
-
0040097482
-
Theory of errors. The Gaussian law and exceptional laws
-
P. LÉVY (1924). Theory of errors. The Gaussian law and exceptional laws. Bull. Soc. Math. France, Vol. 52, pp. 49-85.
-
(1924)
Bull. Soc. Math. France
, vol.52
, pp. 49-85
-
-
Lévy, P.1
-
120
-
-
85039674256
-
-
Gauthier-Villars, Paris, France Second Edition
-
P. LÉVY (1954). Theory of Sums of Random Variables. Gauthier-Villars, Paris, France (Second Edition) 387 pp.
-
(1954)
Theory of Sums of Random Variables
, pp. 387
-
-
Lévy, P.1
-
121
-
-
34250956889
-
A new derivation of exponential laws in probability theory
-
J. W. LINDEBERG (1922). A new derivation of exponential laws in probability theory. Math. Zeitschrift, Vol. 15, pp. 211-225.
-
(1922)
Math. Zeitschrift
, vol.15
, pp. 211-225
-
-
Lindeberg, J.W.1
-
122
-
-
84965126811
-
-
Springer-Verlag, New York, NY Fourth Edition
-
M. LOÈVE (1977). Probability Theory. Volume 1. Springer-Verlag, New York, NY (Fourth Edition). 425 pp.
-
(1977)
Probability Theory
, vol.1
, pp. 425
-
-
Loève, M.1
-
123
-
-
79451473835
-
-
Springer-Verlag, New York, NY Fourth Edition
-
M. LOÈVE (1978). Probability Theory. Volume 2. Springer-Verlag, New York, NY (Fourth Edition). 413 pp.
-
(1978)
Probability Theory
, vol.2
, pp. 413
-
-
Loève, M.1
-
124
-
-
0004203203
-
-
Charles Griffin & Co., London, England
-
E. LUKACS (1960). Characteristic Functions. Charles Griffin & Co., London, England, 387 pp.
-
(1960)
Characteristic Functions
, pp. 387
-
-
Lukacs, E.1
-
126
-
-
0003766457
-
-
Academic Press, New York, NY Second Edition
-
E. LUKACS (1975). Stochastic Convergence. Academic Press, New York, NY (Second Edition). 200 pp.
-
(1975)
Stochastic Convergence
, pp. 200
-
-
Lukacs, E.1
-
127
-
-
0002773602
-
Random numbers fall mainly in the planes
-
G. MARSAGLIA (1968). Random numbers fall mainly in the planes. Proc. Nat. Acad. Sci., Vol. 61, pp. 25-28.
-
(1968)
Proc. Nat. Acad. Sci.
, vol.61
, pp. 25-28
-
-
Marsaglia, G.1
-
128
-
-
0001240132
-
The structure of linear congruential sequences
-
S. K. Zaremba; Academic Press, New York, NY, 1972
-
G. MARSAGLIA (1972). The structure of linear congruential sequences. Applications of Number Theory to Numerical Analysis (Editor, S. K. Zaremba; Academic Press, New York, NY, 1972) pp. 249-285.
-
(1972)
Applications of Number Theory to Numerical Analysis
, pp. 249-285
-
-
Marsaglia, G.1
-
129
-
-
84868013092
-
-
MATHEMATICAL SOCIETY OF JAPAN, Edited by S. Iyanaga and Y. Kawada; Iwanami Shoten Second Edition, MIT Press, Cambridge, MA 1980
-
MATHEMATICAL SOCIETY OF JAPAN (1980). Encyclopedic Dictionary of Mathematics. Volume 1. Edited by S. Iyanaga and Y. Kawada; Iwanami Shoten (Second Edition, 1968); MIT Press, Cambridge, MA (1980). 883 pp.
-
(1968)
Encyclopedic Dictionary of Mathematics
, vol.1
, pp. 883
-
-
-
131
-
-
0012111423
-
A practical approach to the error estimation of quasi-Monte-Carlo integrations. MC & QMC 1998
-
Claremont Graduate School, Claremont, CA, editors, H. Niederreiter, J. Spanier; Springer Verlag, Heidelberg, Germany
-
H. MOROHOSI, M. FUSHIMI (2000). A practical approach to the error estimation of quasi-Monte-Carlo integrations. MC & QMC 1998 (Proc., International Conference on Monte Carlo & Quasi-Monte-Carlo Methods, Claremont Graduate School, Claremont, CA, 1998; editors, H. Niederreiter, J. Spanier; Springer Verlag, Heidelberg, Germany), pp. 377-390.
-
(1998)
Proc., International Conference on Monte Carlo & Quasi-Monte-Carlo Methods
, pp. 377-390
-
-
Morohosi, H.1
Fushimi, M.2
-
132
-
-
4244049434
-
-
Prentice-Hall, Englewood Cliffs, NJ
-
J. R. MUNKRES (1975). Topology-A First Course. Prentice-Hall, Englewood Cliffs, NJ. 413 pp.
-
(1975)
Topology-A First Course
, pp. 413
-
-
Munkres, J.R.1
-
133
-
-
0003668010
-
-
Second Edition. Addison-Wesley, Reading, MA
-
M. E. MUNROE (1971). Measure and Integration. Second Edition. Addison-Wesley, Reading, MA. 290 pp.
-
(1971)
Measure and Integration
, pp. 290
-
-
Munroe, M.E.1
-
134
-
-
0000997571
-
Quasi-Monte Carlo methods and pseudo-random numbers
-
H. NIEDERREITER (1978). Quasi-Monte Carlo methods and pseudo-random numbers. Bull. Amer. Math. Soc., Vol. 84, pp. 957-1041.
-
(1978)
Bull. Amer. Math. Soc.
, vol.84
, pp. 957-1041
-
-
Niederreiter, H.1
-
135
-
-
8344289793
-
Point sets and sequences with small discrepancy
-
H. NIEDERREITER (1987). Point sets and sequences with small discrepancy. Monatsh. Math., Vol. 104, pp. 273-337.
-
(1987)
Monatsh. Math.
, vol.104
, pp. 273-337
-
-
Niederreiter, H.1
-
138
-
-
0000200277
-
A probabilistic result on the discrepancy of a hybrid Monte Carlo sequence and applications
-
G. ÖKTEN (1996). A probabilistic result on the discrepancy of a hybrid Monte Carlo sequence and applications. Monte Carlo Methods & Applications, Vol. 2, pp. 255-270.
-
(1996)
Monte Carlo Methods & Applications
, vol.2
, pp. 255-270
-
-
Ökten, G.1
-
139
-
-
0001303764
-
Error estimation for quasi-Monte-Carlo methods
-
Saltzburg, Austria, editors, P. Hellekalek, G. Larcher; Springer Verlag, Heidelberg, Germany
-
G. ÖKTEN (1998). Error estimation for quasi-Monte-Carlo methods. Random and Quasi-Random Point Sets (Proc., International Conference on Monte Carlo & Quasi-Monte-Carlo Methods, Saltzburg, Austria, 1996; editors, P. Hellekalek, G. Larcher; Springer Verlag, Heidelberg, Germany), pp. 353-368.
-
(1996)
Random and Quasi-random Point Sets (Proc., International Conference on Monte Carlo & Quasi-Monte-Carlo Methods
, pp. 353-368
-
-
Ökten, G.1
-
140
-
-
85039683167
-
Applications of a hybrid Monte Carlo sequence to option pricing. MC & QMC 1998
-
Claremont Graduate School, Claremont, CA, editors, H. Niederreiter, J. Spanier; Springer Verlag, Heidelberg, Germany
-
G. ÖKTEN (2000). Applications of a hybrid Monte Carlo sequence to option pricing. MC & QMC 1998 (Proc., International Conference on Monte Carlo & Quasi-Monte-Carlo Methods, Claremont Graduate School, Claremont, CA, 1998; editors, H. Niederreiter, J. Spanier; Springer Verlag, Heidelberg, Germany), pp. 255-270.
-
(1998)
Proc., International Conference on Monte Carlo & Quasi-Monte-Carlo Methods
, pp. 255-270
-
-
Ökten, G.1
-
141
-
-
84868015219
-
Randomly permuted (t, m, s)-nets and (t, s)-sequences. Monte Carlo & Quasi-Monte-Carlo Methods in Scientific Computing
-
Las Vegas, NV, editors, H. Niederreiter, P. J.-S. Shiue; Springer Verlag, Heidelberg, Germany
-
A. B. OWEN (1995). Randomly permuted (t, m, s)-nets and (t, s)-sequences. Monte Carlo & Quasi-Monte-Carlo Methods in Scientific Computing. (Proc., International Conference on Monte Carlo & Quasi-Monte-Carlo Methods, Las Vegas, NV, 1994; editors, H. Niederreiter, P. J.-S. Shiue; Springer Verlag, Heidelberg, Germany).
-
(1994)
Proc., International Conference on Monte Carlo & Quasi-Monte-Carlo Methods
-
-
Owen, A.B.1
-
142
-
-
0031509503
-
Scrambled net variance for integrals of smooth functions
-
A. B. OWEN (1997a). Scrambled net variance for integrals of smooth functions. Ann. Stat., Vol. 25, pp. 1541-1562.
-
(1997)
Ann. Stat.
, vol.25
, pp. 1541-1562
-
-
Owen, A.B.1
-
143
-
-
0013036522
-
Monte carlo variance of scrambled net quadrature
-
A. B. OWEN (1997b). Monte Carlo variance of scrambled equidistribution quadrature. SIAM J. Numer. Anal., Vol. 34, pp. 1884-1910. (Pubitemid 127463576)
-
(1997)
SIAM Journal on Numerical Analysis
, vol.34
, Issue.5
, pp. 1884-1910
-
-
Owen, A.B.1
-
144
-
-
0031599238
-
Latin supercube sampling for very high dimensional simulations
-
A. B. OWEN (1998). Latin supercube sampling for very high dimensional simulations. ACM Trans. Modeling & Computer Simul., Vol. 8, pp. 71-102.
-
(1998)
ACM Trans. Modeling & Computer Simul.
, vol.8
, pp. 71-102
-
-
Owen, A.B.1
-
145
-
-
0008846507
-
Monte Carlo, quasi-Monte-Carlo, and randomized quasi-Monte-Carlo. MC & QMC 1998
-
Claremont Graduate School, Claremont, CA, editors, H. Niederreiter, J. Spanier; Springer Verlag, Heidelberg, Germany
-
A. B. OWEN (2000). Monte Carlo, quasi-Monte-Carlo, and randomized quasi-Monte-Carlo. MC & QMC 1998 (Proc., International Conference on Monte Carlo & Quasi-Monte-Carlo Methods, Claremont Graduate School, Claremont, CA, 1998; editors, H. Niederreiter, J. Spanier; Springer Verlag, Heidelberg, Germany), pp. 86-97.
-
(1998)
Proc., International Conference on Monte Carlo & Quasi-Monte-Carlo Methods
, pp. 86-97
-
-
Owen, A.B.1
-
148
-
-
84868014133
-
Minimum variance Monte Carlo importance sampling with parametric dependence
-
M. M. H. RAGHEB, J. H. HALTON, C. W. MAYNARD (1981). Minimum variance Monte Carlo importance sampling with parametric dependence. Atomkernenergie- Kerntechnik, Vol. 37, pp. 188-193
-
(1981)
Atomkernenergie-kerntechnik
, vol.37
, pp. 188-193
-
-
Ragheb, M.M.H.1
Halton, J.H.2
Maynard, C.W.3
-
152
-
-
0004155375
-
-
John Wiley & Sons, New York, NY
-
J. RIORDAN (1968). Combinatorial Identities. John Wiley & Sons, New York, NY. 256 pp.
-
(1968)
Combinatorial Identities
, pp. 256
-
-
Riordan, J.1
-
153
-
-
0002851522
-
On irregularities of distribution
-
K. F. ROTH (1954). On irregularities of distribution. Mathematika, Vol. 1, pp. 73-79.
-
(1954)
Mathematika
, vol.1
, pp. 73-79
-
-
Roth, K.F.1
-
156
-
-
2042548005
-
Error trends in quasi-Monte-Carlo integration
-
CH. SCHLIER (2003). Error trends in quasi-Monte-Carlo integration. Computer Physics Communications, Vol. 159, pp. 93-1050.
-
(2003)
Computer Physics Communications
, vol.159
, pp. 93-1050
-
-
Schlier, Ch.1
-
157
-
-
2042493187
-
Discrepancy behaviour in the non-asymptotic regime
-
CH. SCHLIER (2004). Discrepancy behaviour in the non-asymptotic regime. Applied Numerical Mathematics, Vol. 50, pp. 227-238.
-
(2004)
Applied Numerical Mathematics
, vol.50
, pp. 227-238
-
-
Schlier, Ch.1
-
158
-
-
0003391815
-
-
Allyn & Bacon, Boston, MA
-
H. SCHUBERT (1968). Topology. Allyn & Bacon, Boston, MA. 358 pp.
-
(1968)
Topology
, pp. 358
-
-
Schubert, H.1
-
159
-
-
0001352321
-
The distribution of points in a cube and the approximate evaluation of integrals
-
I. M. SOBOL' (1967). The distribution of points in a cube and the approximate evaluation of integrals. Zh. Vychisl. Mat. I Mat. Fiz., Vol. 7, pp. 784-802.
-
(1967)
Zh. Vychisl. Mat. i Mat. Fiz.
, vol.7
, pp. 784-802
-
-
Sobol, I.M.1
-
163
-
-
0004200722
-
-
Academic Press, New York, NY
-
W. F. STOUT (1974). Almost Sure Convergence. Academic Press, New York, NY. 381 pp.
-
(1974)
Almost Sure Convergence
, pp. 381
-
-
Stout, W.F.1
-
164
-
-
0003674177
-
-
Prindle, Weber & Schmidt, Boston, MA Second Edition
-
E. W. SWOKOWSKI (1979). Calculus-With Analytic Geometry. Prindle, Weber & Schmidt, Boston, MA (Second Edition). 1085 pp.
-
(1979)
Calculus-with Analytic Geometry
, pp. 1085
-
-
Swokowski, E.W.1
-
165
-
-
0004088592
-
-
Holt, Rinehart & Winston, New York, NY
-
W. J. THRON (1966). Topological Structures. Holt, Rinehart & Winston, New York, NY. 240 pp.
-
(1966)
Topological Structures
, pp. 240
-
-
Thron, W.J.1
-
168
-
-
0009366897
-
-
Academic Press, New York, NY
-
N. YA. VILENKIN (1971). Combinatorics. Academic Press, New York, NY. 296 pp.
-
(1971)
Combinatorics
, pp. 296
-
-
Vilenkin, N.Ya.1
-
171
-
-
84868006611
-
Effective error estimates for quasi-Monte-Carlo computations
-
Invited lecture, University of North Carolina, Chapel Hill, NC, 28 July 1997
-
T. T. WARNOCK (1997). Effective error estimates for quasi-Monte-Carlo computations. Invited lecture, Joint Statistics/Operations Research/Computer Science Colloquium, University of North Carolina, Chapel Hill, NC, 28 July 1997.
-
(1997)
Joint Statistics/Operations Research/Computer Science Colloquium
-
-
Warnock, T.T.1
-
175
-
-
0010797727
-
The mathematical basis of Monte Carlo and quasi-Monte Carlo methods
-
S. K. ZAREMBA (1968a). The mathematical basis of Monte Carlo and quasi-Monte Carlo methods. SIAM Review, Vol. 10, pp. 303-314.
-
(1968)
SIAM Review
, vol.10
, pp. 303-314
-
-
Zaremba, S.K.1
-
176
-
-
0002548979
-
Some applications of multidimensional integration by parts
-
S. K. ZAREMBA (1968b). Some applications of multidimensional integration by parts. Ann. Polon. Math., Vol. 21, pp. 85-96.
-
(1968)
Ann. Polon. Math.
, vol.21
, pp. 85-96
-
-
Zaremba, S.K.1
|