메뉴 건너뛰기




Volumn 7, Issue , 1998, Pages 1-49

Monte Carlo and quasi-Monte Carlo methods

Author keywords

[No Author keywords available]

Indexed keywords


EID: 85011514513     PISSN: 09624929     EISSN: 14740508     Source Type: Journal    
DOI: 10.1017/S0962492900002804     Document Type: Article
Times cited : (1285)

References (55)
  • 1
    • 0002809516 scopus 로고    scopus 로고
    • A comparison of some Monte Carlo and quasi Monte Carlo techniques for option pricing
    • (Larcher G., Niederreiter H., Hellekalek P. and Zinterhof P., eds), Springer
    • Acworth P., Broadie M. and Glasserman P. (1997), A comparison of some Monte Carlo and quasi Monte Carlo techniques for option pricing, in Monte Carlo and Quasi-Monte Carlo Methods 1996 (Larcher G., Niederreiter H., Hellekalek P. and Zinterhof P., eds), Springer.
    • (1997) Monte Carlo and Quasi-Monte Carlo Methods 1996
    • Acworth, P.1    Broadie, M.2    Glasserman, P.3
  • 2
    • 38249019927 scopus 로고
    • Application of well-distributed sequences to the numerical simulation of the Boltzmann equation
    • Babovsky H., Gropengiesser F., Neunzert H., Struckmeier J. and Wiesen J. (1990), ‘Application of well-distributed sequences to the numerical simulation of the Boltzmann equation’, J. Comput. Appl. Math. 31, 15–22.
    • (1990) J. Comput. Appl. Math. , vol.31 , pp. 15-22
    • Babovsky, H.1    Gropengiesser, F.2    Neunzert, H.3    Struckmeier, J.4    Wiesen, J.5
  • 3
    • 0001076950 scopus 로고
    • Fluid dynamic limits of kinetic equations: I. Formal derivations
    • Bardos C., Golse F. and Levermore C. D. (1991), ‘Fluid dynamic limits of kinetic equations: I. Formal derivations’, J. Statist. Phys. 63, 323–344.
    • (1991) J. Statist. Phys. , vol.63 , pp. 323-344
    • Bardos, C.1    Golse, F.2    Levermore, C.D.3
  • 4
    • 84990619144 scopus 로고
    • Fluid dynamic limits of kinetic equations: II. Convergence proofs for the Boltzmann equation
    • Bardos C., Golse F. and Levermore C. D. (1993), ‘Fluid dynamic limits of kinetic equations: II. Convergence proofs for the Boltzmann equation’, Comm. Pure Appl. Math. 46, 667–753.
    • (1993) Comm. Pure Appl. Math. , vol.46 , pp. 667-753
    • Bardos, C.1    Golse, F.2    Levermore, C.D.3
  • 6
    • 0017956227 scopus 로고
    • Monte Carlo simulation of gas flows
    • Bird G. A. (1978), ‘Monte Carlo simulation of gas flows’, Ann. Rev. Fluid Mech. 10, 11–31.
    • (1978) Ann. Rev. Fluid Mech. , vol.10 , pp. 11-31
    • Bird, G.A.1
  • 7
    • 0010115469 scopus 로고
    • The asymptotic diffusion limit of a linear discontinuous discretization of a two-dimensional linear transport equation
    • Borgers C., Larsen E. W. and Adams M. L. (1992), ‘The asymptotic diffusion limit of a linear discontinuous discretization of a two-dimensional linear transport equation’ J. Comput. Phys. 98, 285–300.
    • (1992) J. Comput. Phys. , vol.98 , pp. 285-300
    • Borgers, C.1    Larsen, E.W.2    Adams, M.L.3
  • 8
    • 0028756686 scopus 로고
    • Algorithm 738 – Programs to generate Niederreiter's discrepancy sequences
    • Bratley P., Fox B. L. and Niederreiter H. (1994), ‘Algorithm 738 – Programs to generate Niederreiter's discrepancy sequences’, ACM Trans. Math. Software 20, 494–495.
    • (1994) ACM Trans. Math. Software , vol.20 , pp. 494-495
    • Bratley, P.1    Fox, B.L.2    Niederreiter, H.3
  • 9
    • 26844444980 scopus 로고
    • Fluid dynamics and the Boltzmann equation
    • (Montroll E. W. and Lebowitz J. L., eds), of Studies in Statistical Mechanics, North Holland
    • Caflisch R. E. (1983), Fluid dynamics and the Boltzmann equation, in Nonequilibrium Phenomena I: The Boltzmann equation (Montroll E. W. and Lebowitz J. L., eds), Vol. 10 of Studies in Statistical Mechanics, North Holland, pp. 193–223.
    • (1983) Nonequilibrium Phenomena I: The Boltzmann equation , vol.10 , pp. 193-223
    • Caflisch, R.E.1
  • 10
    • 0001407297 scopus 로고    scopus 로고
    • Uniformly accurate schemes for hyperbolic systems with relaxation
    • (a)
    • Caflisch R. E., Jin S. and Russo G. (1997a), ‘Uniformly accurate schemes for hyperbolic systems with relaxation’, SIAM J. Numer. Anal. 34, 246–281.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 246-281
    • Caflisch, R.E.1    Jin, S.2    Russo, G.3
  • 11
    • 0003008716 scopus 로고    scopus 로고
    • Valuation of mortgage-backed securities using Brownian bridges to reduce effective dimension
    • (b)
    • Caflisch R. E., Morokoff W. and Owen A. B. (1997b), ‘Valuation of mortgage-backed securities using Brownian bridges to reduce effective dimension’, J. Comput. Finance 1, 27–46.
    • (1997) J. Comput. Finance , vol.1 , pp. 27-46
    • Caflisch, R.E.1    Morokoff, W.2    Owen, A.B.3
  • 14
    • 84990591606 scopus 로고
    • Incompressible Navier–Stokes and Euler limits of the Boltzmann equation
    • De Masi A., Esposito R. and Lebowitz J. L. (1989), ‘Incompressible Navier–Stokes and Euler limits of the Boltzmann equation’, Comm. Pure Appl. Math. 42, 1189–1214.
    • (1989) Comm. Pure Appl. Math. , vol.42 , pp. 1189-1214
    • De Masi, A.1    Esposito, R.2    Lebowitz, J.L.3
  • 15
    • 0001013260 scopus 로고
    • Discrépance de suites associées à un système de numération (en dimension s)
    • Faure H. (1982), ‘Discrépance de suites associées à un système de numération (en dimension s)’, Acta Arithmetica 41, 337–351.
    • (1982) Acta Arithmetica , vol.41 , pp. 337-351
    • Faure, H.1
  • 17
    • 0000677613 scopus 로고    scopus 로고
    • Relaxation schemes for nonlinear kinetic equations
    • Gabetta E., Pareschi L. and Toscani G. (1997), ‘Relaxation schemes for nonlinear kinetic equations’, SIAM J. Numer. Anal. 34, 2168–2194.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 2168-2194
    • Gabetta, E.1    Pareschi, L.2    Toscani, G.3
  • 18
    • 0001776391 scopus 로고
    • Investigations of the motion of discrete-velocity gases
    • (Muntz E. P., Weaver D. P. and Campbell D. H., eds), Vol. 118 of Progress in Aeronautics and Astronautics, Proceedings of the 16th International Symposium on Rarefied Gas Dynamics
    • Goldstein D., Sturtevant B. and Broadwell J. E. (1988), Investigations of the motion of discrete-velocity gases, in Rarefied Gas Dynamics: Theoretical and Computational Techniques (Muntz E. P., Weaver D. P. and Campbell D. H., eds), Vol. 118 of Progress in Aeronautics and Astronautics, Proceedings of the 16th International Symposium on Rarefied Gas Dynamics, pp. 100–117.
    • (1988) Rarefied Gas Dynamics: Theoretical and Computational Techniques , pp. 100-117
    • Goldstein, D.1    Sturtevant, B.2    Broadwell, J.E.3
  • 19
    • 0002020770 scopus 로고
    • On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals
    • Halton J. H. (1960), ‘On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals’, Numer. Math. 2, 84–90.
    • (1960) Numer. Math. , vol.2 , pp. 84-90
    • Halton, J.H.1
  • 21
    • 84968515112 scopus 로고
    • A method for numerical integration
    • Haselgrove C. (1961), ‘A method for numerical integration’, Math. Comput. 15, 323–337.
    • (1961) Math. Comput. , vol.15 , pp. 323-337
    • Haselgrove, C.1
  • 22
    • 0030259017 scopus 로고    scopus 로고
    • The mean square discrepancy of randomized nets
    • Hickernell F. J. (1996), ‘The mean square discrepancy of randomized nets’, ACM Trans. Model. Comput. Simul. 6, 274–296.
    • (1996) ACM Trans. Model. Comput. Simul. , vol.6 , pp. 274-296
    • Hickernell, F.J.1
  • 23
    • 0032345316 scopus 로고    scopus 로고
    • A generalized discrepancy and quadrature error bound
    • Hickernell F. J. (1998), ‘A generalized discrepancy and quadrature error bound’, Math. Comput. 67, 299–322.
    • (1998) Math. Comput. , vol.67 , pp. 299-322
    • Hickernell, F.J.1
  • 26
    • 0000397910 scopus 로고
    • Fully-discrete numerical transfer in diffusive regimes
    • Jin S. and Levermore C. D. (1993), ‘Fully-discrete numerical transfer in diffusive regimes’, Transp. Theory Statist. Phys., 22, 739–791.
    • (1993) Transp. Theory Statist. Phys. , vol.22 , pp. 739-791
    • Jin, S.1    Levermore, C.D.2
  • 27
    • 85011531937 scopus 로고    scopus 로고
    • Diffusive relaxation schemes for discrete-velocity kinetic equations
    • Preprint
    • Jin S., Pareschi L. and Toscani G. (1998), ‘Diffusive relaxation schemes for discrete-velocity kinetic equations’. Preprint.
    • (1998)
    • Jin, S.1    Pareschi, L.2    Toscani, G.3
  • 31
    • 0000833486 scopus 로고
    • Null-collision technique in the direct-simulation Monte Carlo method
    • Koura K. (1986), ‘Null-collision technique in the direct-simulation Monte Carlo method’, Phys. Fluids 29, 3509–3511.
    • (1986) Phys. Fluids , vol.29 , pp. 3509-3511
    • Koura, K.1
  • 33
    • 0020929962 scopus 로고
    • Diffusion-synthetic acceleration methods for discrete-ordinates problems
    • Larsen E. W. (1984), ‘Diffusion-synthetic acceleration methods for discrete-ordinates problems’, Transp. Theory Statist. Phys. 13, 107–126.
    • (1984) Transp. Theory Statist. Phys. , vol.13 , pp. 107-126
    • Larsen, E.W.1
  • 34
    • 0000718834 scopus 로고
    • Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes
    • Larsen E. W., Morel J. E. and Miller W. F. (1987), ‘Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes’, J. Comput. Phys. 69, 283–324.
    • (1987) J. Comput. Phys. , vol.69 , pp. 283-324
    • Larsen, E.W.1    Morel, J.E.2    Miller, W.F.3
  • 35
    • 0011636441 scopus 로고
    • A new algorithm for adaptive multidimensional integration
    • Lepage G. (1978), ‘A new algorithm for adaptive multidimensional integration’, J. Comput. Phys. 27, 192–203.
    • (1978) J. Comput. Phys. , vol.27 , pp. 192-203
    • Lepage, G.1
  • 36
    • 0026168942 scopus 로고
    • Normal (Gaussian) random variables for supercomputers
    • Marsaglia G. (1991), ‘Normal (Gaussian) random variables for supercomputers’, J. Supercomputing 5, 49–55.
    • (1991) J. Supercomputing , vol.5 , pp. 49-55
    • Marsaglia, G.1
  • 37
    • 0027805257 scopus 로고
    • A quasi-Monte Carlo approach to particle simulation of the heat equation
    • Morokoff W. and Caflisch R. E. (1993), ‘A quasi-Monte Carlo approach to particle simulation of the heat equation’, SIAM J. Numer. Anal. 30, 1558–1573.
    • (1993) SIAM J. Numer. Anal. , vol.30 , pp. 1558-1573
    • Morokoff, W.1    Caflisch, R.E.2
  • 38
    • 0001563525 scopus 로고
    • Quasi-random sequences and their discrepancies
    • Morokoff W. and Caflisch R. E. (1994), ‘Quasi-random sequences and their discrepancies’, SIAM J. Sci. Statist. Comput. 15, 1251–1279.
    • (1994) SIAM J. Sci. Statist. Comput. , vol.15 , pp. 1251-1279
    • Morokoff, W.1    Caflisch, R.E.2
  • 39
    • 0001243365 scopus 로고
    • Quasi-Monte Carlo integration
    • Morokoff W. and Caflisch R. E. (1995), ‘Quasi-Monte Carlo integration’, J. Comput. Phys. 122, 218–230.
    • (1995) J. Comput. Phys. , vol.122 , pp. 218-230
    • Morokoff, W.1    Caflisch, R.E.2
  • 40
    • 0002622180 scopus 로고    scopus 로고
    • Smoothness and dimension reduction in quasi-Monte Carlo methods
    • Moskowitz B. and Caflisch R. E. (1996), ‘Smoothness and dimension reduction in quasi-Monte Carlo methods’, J. Math. Comput. Modeling 23, 37–54.
    • (1996) J. Math. Comput. Modeling , vol.23 , pp. 37-54
    • Moskowitz, B.1    Caflisch, R.E.2
  • 41
    • 0040268725 scopus 로고
    • Theoretical basis of the direct simulation Monte Carlo method
    • (Boffi V. and Cercignani C., eds)
    • Nanbu K. (1986), Theoretical basis of the direct simulation Monte Carlo method, in Proceedings of the 15th International Symposium on Rarefied Gas Dynamics (Boffi V. and Cercignani C., eds), Vol. I, pp. 369–383.
    • (1986) Proceedings of the 15th International Symposium on Rarefied Gas Dynamics , vol.1 , pp. 369-383
    • Nanbu, K.1
  • 43
    • 0001491057 scopus 로고
    • Randomly permuted (t, m, s)-nets and (t, s)-sequences
    • (Niederreiter H. and Shiue P. J.-S., eds), Springer, New York
    • Owen A. B. (1995), Randomly permuted (t, m, s)-nets and (t, s)-sequences, in Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (Niederreiter H. and Shiue P. J.-S., eds), Springer, New York, pp. 299–317.
    • (1995) Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing , pp. 299-317
    • Owen, A.B.1
  • 44
    • 0013036522 scopus 로고    scopus 로고
    • Monte Carlo variance of scrambled net quadrature
    • Owen A. B. (1997), ‘Monte Carlo variance of scrambled net quadrature’, SIAM J. Numer. Anal. 34, 1884–1910.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 1884-1910
    • Owen, A.B.1
  • 45
    • 85011486014 scopus 로고    scopus 로고
    • Scrambled net variance for integrals of smooth functions
    • In press
    • Owen A. B. (1998), ‘Scrambled net variance for integrals of smooth functions’, Ann. Statist. In press.
    • (1998) Ann. Statist.
    • Owen, A.B.1
  • 46
    • 0026768474 scopus 로고
    • Portable random number generators
    • Press W. H. and Teukolsky S. A. (1992), ‘Portable random number generators’, Comput. Phys. 6, 522–524.
    • (1992) Comput. Phys. , vol.6 , pp. 522-524
    • Press, W.H.1    Teukolsky, S.A.2
  • 48
    • 0009965365 scopus 로고
    • Generation of normal variates with given sample and mean variance
    • Pullin D. I. (1979), ‘Generation of normal variates with given sample and mean variance’, J. Statist. Comput. Simul. 9, 303–309.
    • (1979) J. Statist. Comput. Simul. , vol.9 , pp. 303-309
    • Pullin, D.I.1
  • 49
    • 0001352321 scopus 로고
    • The distribution of points in a cube and the accurate evaluation of integrals
    • In Russian.
    • Sobol I. M. ' (1967), ‘The distribution of points in a cube and the accurate evaluation of integrals’, Zh. Vychisl. Mat. Mat. Fiz. 7, 784–802. In Russian.
    • (1967) Zh. Vychisl. Mat. Mat. Fiz. , vol.7 , pp. 784-802
    • Sobol, I.M.1
  • 50
    • 49349129696 scopus 로고
    • Uniformly distributed sequences with additional uniformity property
    • Sobol I. M. ' (1976), ‘Uniformly distributed sequences with additional uniformity property’, USSR Comput. Math. Math. Phys. 16, 1332–1337.
    • (1976) USSR Comput. Math. Math. Phys. , vol.16 , pp. 1332-1337
    • Sobol, I.M.1
  • 51
    • 0028387701 scopus 로고
    • Quasi-random methods for estimating integrals using relatively small samples
    • Spanier J. and Maize E. H. (1994), ‘Quasi-random methods for estimating integrals using relatively small samples’, SIAM Rev. 36, 18–44.
    • (1994) SIAM Rev , vol.36 , pp. 18-44
    • Spanier, J.1    Maize, E.H.2
  • 52
    • 34249834360 scopus 로고
    • A convergence proof for Bird's Direct Simulation Monte Carlo method for the Boltzmann equation
    • Wagner W. (1992), ‘A convergence proof for Bird's Direct Simulation Monte Carlo method for the Boltzmann equation’, J. Statist. Phys. 66, 1011–1044.
    • (1992) J. Statist. Phys. , vol.66 , pp. 1011-1044
    • Wagner, W.1
  • 53
    • 84967790439 scopus 로고
    • Average case complexity of multivariate integration
    • Woźniakowski H. (1991), ‘Average case complexity of multivariate integration’, Bull. Amer. Math. Soc. 24, 185–194.
    • (1991) Bull. Amer. Math. Soc. , vol.24 , pp. 185-194
    • Woźniakowski, H.1
  • 54
    • 21844527203 scopus 로고
    • A construction of low-discrepancy sequences using global function fields
    • Xing C. P. and Niederreiter H. (1995), ‘A construction of low-discrepancy sequences using global function fields’, Acta Arithmetica 73, 87–102.
    • (1995) Acta Arithmetica , vol.73 , pp. 87-102
    • Xing, C.P.1    Niederreiter, H.2
  • 55
    • 0010797727 scopus 로고
    • The mathematical basis of Monte Carlo and quasi-Monte Carlo methods
    • Zaremba S. K. (1968), ‘The mathematical basis of Monte Carlo and quasi-Monte Carlo methods’, SIAM Rev. 10, 303–314.
    • (1968) SIAM Rev , vol.10 , pp. 303-314
    • Zaremba, S.K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.