메뉴 건너뛰기




Volumn 167, Issue 2, 2015, Pages 143-171

Functions of bounded variation, signed measures, and a general Koksma-Hlawka inequality

Author keywords

Completely monotone function; Discrepancy theory; Function of bounded variation; Quasi Monte Carlo method; Signed measure

Indexed keywords


EID: 84921831084     PISSN: 00651036     EISSN: None     Source Type: Journal    
DOI: 10.4064/aa167-2-4     Document Type: Article
Times cited : (59)

References (52)
  • 1
    • 0001505048 scopus 로고
    • Properties of functions f(x, y) of bounded variation
    • C. R. Adams and J. A. Clarkson, Properties of functions f(x, y) of bounded variation, Trans. Amer. Math. Soc. 36 (1934), 711-730.
    • (1934) Trans. Amer. Math. Soc. , vol.36 , pp. 711-730
    • Adams, C.R.1    Clarkson, J.A.2
  • 2
    • 84907386116 scopus 로고    scopus 로고
    • Low-discrepancy point sets for non-uniform measures
    • C. Aistleitner and J. Dick, Low-discrepancy point sets for non-uniform measures, Acta Arith. 163 (2014), 345-369.
    • (2014) Acta Arith. , vol.163 , pp. 345-369
    • Aistleitner, C.1    Dick, J.2
  • 4
    • 0000329787 scopus 로고
    • Some upper bounds in the theory of irregularities of distribution
    • J. Beck, Some upper bounds in the theory of irregularities of distribution, Acta Arith. 43 (1983), 115-130.
    • (1983) Acta Arith. , vol.43 , pp. 115-130
    • Beck, J.1
  • 5
    • 84879422273 scopus 로고    scopus 로고
    • On Roth's orthogonal function method in discrepancy theory
    • D. Bilyk, On Roth's orthogonal function method in discrepancy theory, Unif. Distrib. Theory 6 (2011), 143-184.
    • (2011) Unif. Distrib. Theory , vol.6 , pp. 143-184
    • Bilyk, D.1
  • 6
    • 41049098063 scopus 로고    scopus 로고
    • On the small ball inequality in all dimensions
    • D. Bilyk, M. T. Lacey, and A. Vagharshakyan, On the small ball inequality in all dimensions, J. Funct. Anal. 254 (2008), 2470-2502.
    • (2008) J. Funct. Anal. , vol.254 , pp. 2470-2502
    • Bilyk, D.1    Lacey, M.T.2    Vagharshakyan, A.3
  • 7
    • 38249019397 scopus 로고
    • On effective computation of expectations in large or infinite dimension
    • N. Bouleau, On effective computation of expectations in large or infinite dimension, J. Comput. Appl. Math. 31 (1990), 23-34.
    • (1990) J. Comput. Appl. Math. , vol.31 , pp. 23-34
    • Bouleau, N.1
  • 14
    • 0003331047 scopus 로고    scopus 로고
    • Sequences, discrepancies and applications
    • Springer, Berlin
    • M. Drmota and R. F. Tichy, Sequences, Discrepancies and Applications, Lecture Notes in Math. 1651, Springer, Berlin, 1997.
    • (1997) Lecture Notes in Math. , pp. 1651
    • Drmota, M.1    Tichy, R.F.2
  • 15
    • 0036614289 scopus 로고    scopus 로고
    • Discrepancy and the error in integration
    • M. Götz, Discrepancy and the error in integration, Monatsh. Math. 136 (2002), 99-121.
    • (2002) Monatsh. Math. , vol.136 , pp. 99-121
    • Götz, M.1
  • 16
    • 68349126329 scopus 로고    scopus 로고
    • Non-uniform low-discrepancy sequence generation and integration of singular integrands
    • Springer, Berlin
    • J. Hartinger and R. Kainhofer, Non-uniform low-discrepancy sequence generation and integration of singular integrands, in: Monte Carlo and Quasi-Monte Carlo Methods 2004, Springer, Berlin, 2006, 163-179.
    • (2004) Monte Carlo and Quasi-Monte Carlo Methods , pp. 163-179
    • Hartinger, J.1    Kainhofer, R.2
  • 17
    • 4444243396 scopus 로고    scopus 로고
    • Quasi-Monte Carlo algorithms for unbounded, weighted integration problems
    • J. Hartinger, R. F. Kainhofer, and R. F. Tichy, Quasi-Monte Carlo algorithms for unbounded, weighted integration problems, J. Complexity 20 (2004), 654-668.
    • (2004) J. Complexity , vol.20 , pp. 654-668
    • Hartinger, J.1    Kainhofer, R.F.2    Tichy, R.F.3
  • 18
    • 0035649406 scopus 로고    scopus 로고
    • The inverse of the star-discrepancy depends linearly on the dimension
    • S. Heinrich, E. Novak, G. W. Wasilkowski, and H. Wozniakowski, The inverse of the star-discrepancy depends linearly on the dimension, Acta Arith. 96 (2001), 279-302.
    • (2001) Acta Arith. , vol.96 , pp. 279-302
    • Heinrich, S.1    Novak, E.2    Wasilkowski, G.W.3    Wozniakowski, H.4
  • 19
    • 0000489595 scopus 로고
    • Funktionen von beschränkter Variation in der Theorie der Gleichverteilung
    • E. Hlawka, Funktionen von beschränkter Variation in der Theorie der Gleichverteilung, Ann. Mat. Pura Appl. (4) 54 (1961), 325-333.
    • (1961) Ann. Mat. Pura Appl. (4) , vol.54 , pp. 325-333
    • Hlawka, E.1
  • 20
    • 0039439759 scopus 로고
    • A transformation of equidistributed sequences
    • Proc. Sympos., Univ. Montréal, Montréal, QC, Academic Press, New York
    • E. Hlawka and R. Mück, A transformation of equidistributed sequences, in: Applications of Number Theory to Numerical Analysis (Proc. Sympos., Univ. Montréal, Montréal, QC, 1971), Academic Press, New York, 1972, 371-388.
    • (1971) Applications of Number Theory to Numerical Analysis , pp. 371-388
    • Hlawka, E.1    Mück, R.2
  • 21
    • 0004790992 scopus 로고
    • Über eine Transformation von gleichverteilten Folgen. II
    • E. Hlawka und R. Mück, Über eine Transformation von gleichverteilten Folgen. II, Computing (Arch. Elektron. Rechnen) 9 (1972), 127-138.
    • (1972) Computing (Arch. Elektron. Rechnen) , vol.9 , pp. 127-138
    • Hlawka, E.1    Mück, R.2
  • 23
    • 84921877385 scopus 로고    scopus 로고
    • Probability
    • Amer. Math. Soc., Providence, RI
    • D. Khoshnevisan, Probability, Grad. Stud. Math. 80, Amer. Math. Soc., Providence, RI, 2007.
    • (2007) Grad. Stud. Math. , vol.80
    • Khoshnevisan, D.1
  • 24
    • 0002745071 scopus 로고
    • A general theorem from the theory of uniform distribution modulo 1
    • (in Dutch)
    • J. F. Koksma, A general theorem from the theory of uniform distribution modulo 1, Mathematica Zutphen. B 11 (1942), 7-11 (in Dutch).
    • (1942) Mathematica Zutphen. B , vol.11 , pp. 7-11
    • Koksma, J.F.1
  • 27
    • 0001912453 scopus 로고    scopus 로고
    • Remarks on the total variation of functions of several variables and on a multidimensional analogue of Helly's choice principle
    • (in Russian)
    • A. S. Leonov, Remarks on the total variation of functions of several variables and on a multidimensional analogue of Helly's choice principle, Mat. Zametki 63 (1998), 69-80 (in Russian).
    • (1998) Mat. Zametki , vol.63 , pp. 69-80
    • Leonov, A.S.1
  • 30
    • 0037716324 scopus 로고    scopus 로고
    • Some current issues in quasi-Monte Carlo methods
    • H. Niederreiter, Some current issues in quasi-Monte Carlo methods, J. Complexity 19 (2003), 428-433.
    • (2003) J. Complexity , vol.19 , pp. 428-433
    • Niederreiter, H.1
  • 35
    • 0033215183 scopus 로고    scopus 로고
    • Error reduction techniques in quasi-Monte Carlo integration
    • G. Ökten, Error reduction techniques in quasi-Monte Carlo integration, Math. Comput. Modelling 30, no. 7-8, (1999), 61-69.
    • (1999) Math. Comput. Modelling , vol.30 , Issue.7-8 , pp. 61-69
    • Ökten, G.1
  • 37
    • 84858407875 scopus 로고    scopus 로고
    • A theoretical view on transforming low-discrepancy sequences from a cube to a simplex
    • T. Pillards and R. Cools, A theoretical view on transforming low-discrepancy sequences from a cube to a simplex, Monte Carlo Methods Appl. 10 (2004), 511-529.
    • (2004) Monte Carlo Methods Appl. , vol.10 , pp. 511-529
    • Pillards, T.1    Cools, R.2
  • 38
    • 8344258050 scopus 로고    scopus 로고
    • Transforming low-discrepancy sequences from a cube to a simplex
    • T. Pillards and R. Cools, Transforming low-discrepancy sequences from a cube to a simplex, J. Comput. Appl. Math. 174 (2005), 29-42.
    • (2005) J. Comput. Appl. Math. , vol.174 , pp. 29-42
    • Pillards, T.1    Cools, R.2
  • 39
    • 67649118651 scopus 로고    scopus 로고
    • A mixed Monte Carlo and quasi-Monte Carlo sequence for multidimensional integral estimation
    • A. V. Rosca, A mixed Monte Carlo and quasi-Monte Carlo sequence for multidimensional integral estimation, Acta Univ. Apulensis Math. Inform. 14 (2007), 141-160.
    • (2007) Acta Univ. Apulensis Math. Inform. , vol.14 , pp. 141-160
    • Rosca, A.V.1
  • 40
    • 68149155961 scopus 로고    scopus 로고
    • Generation of non-uniform low-discrepancy sequences in the multidimensional case
    • N. Rosca, Generation of non-uniform low-discrepancy sequences in the multidimensional case, Rev. Anal. Numér. Théor. Approx. 35 (2006), 207-219.
    • (2006) Rev. Anal. Numér. Théor. Approx. , vol.35 , pp. 207-219
    • Rosca, N.1
  • 41
    • 84921872710 scopus 로고    scopus 로고
    • A combined Monte Carlo and quasi-Monte Carlo method with applications to option pricing
    • N. C. Rosca, A combined Monte Carlo and quasi-Monte Carlo method with applications to option pricing, Acta Univ. Apulensis Math. Inform. 19 (2009), 217-235.
    • (2009) Acta Univ. Apulensis Math. Inform. , vol.19 , pp. 217-235
    • Rosca, N.C.1
  • 42
    • 0000301907 scopus 로고
    • Remarks on a multivariate transformation
    • M. Rosenblatt, Remarks on a multivariate transformation, Ann. Math. Statist. 23 (1952), 470-472.
    • (1952) Ann. Math. Statist. , vol.23 , pp. 470-472
    • Rosenblatt, M.1
  • 44
    • 84875411789 scopus 로고    scopus 로고
    • A direct inversion method for non-uniform quasirandom point sequences
    • C. Schretter and H. Niederreiter, A direct inversion method for non-uniform quasirandom point sequences, Monte Carlo Methods Appl. 19 (2013), 1-9.
    • (2013) Monte Carlo Methods Appl. , vol.19 , pp. 1-9
    • Schretter, C.1    Niederreiter, H.2
  • 46
    • 84858392885 scopus 로고    scopus 로고
    • Quasi-Monte Carlo methods for integral equations
    • Salzburg, Lecture Notes in Statist. 127, Springer, New York
    • J. Spanier and L. Li, Quasi-Monte Carlo methods for integral equations, in: Monte Carlo and Quasi-Monte Carlo Methods 1996 (Salzburg), Lecture Notes in Statist. 127, Springer, New York, 1998, 398-414.
    • (1996) Monte Carlo and Quasi-Monte Carlo Methods , pp. 398-414
    • Spanier, J.1    Li, L.2
  • 47
    • 0028387701 scopus 로고
    • Quasi-random methods for estimating integrals using relatively small samples
    • J. Spanier and E. H. Maize, Quasi-random methods for estimating integrals using relatively small samples, SIAM Rev. 36 (1994), 18-44.
    • (1994) SIAM Rev. , vol.36 , pp. 18-44
    • Spanier, J.1    Maize, E.H.2
  • 48
    • 84858282631 scopus 로고    scopus 로고
    • How do path generation methods affect the accuracy of quasi-Monte Carlo methods for problems in finance?
    • X. Wang and K. S. Tan, How do path generation methods affect the accuracy of quasi-Monte Carlo methods for problems in finance?, J. Complexity 28 (2012), 250-277.
    • (2012) J. Complexity , vol.28 , pp. 250-277
    • Wang, X.1    Tan, K.S.2
  • 49
    • 84874172227 scopus 로고    scopus 로고
    • Pricing and hedging with discontinuous functions: Quasi- Monte Carlo methods and dimension reduction
    • X. Wang and K. S. Tan, Pricing and hedging with discontinuous functions: Quasi- Monte Carlo methods and dimension reduction, Management Sci. 59 (2013), 376-389.
    • (2013) Management Sci. , vol.59 , pp. 376-389
    • Wang, X.1    Tan, K.S.2
  • 50
    • 0009743812 scopus 로고    scopus 로고
    • Variation of product function and numerical solution of some partial differential equations by low-discrepancy sequences
    • Y.-J. Xiao, Variation of product function and numerical solution of some partial differential equations by low-discrepancy sequences, Monte Carlo Methods Appl. 2 (1996), 321-330.
    • (1996) Monte Carlo Methods Appl. , vol.2 , pp. 321-330
    • Xiao, Y.-J.1
  • 52
    • 0002548979 scopus 로고
    • Some applications of multidimensional integration by parts
    • S. K. Zaremba, Some applications of multidimensional integration by parts, Ann. Polon. Math. 21 (1968), 85-96.
    • (1968) Ann. Polon. Math. , vol.21 , pp. 85-96
    • Zaremba, S.K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.