A Retrospective and Prospective Survey of the Monte Carlo Method

Abstract

Next article A Retrospective and Prospective Survey of the Monte Carlo MethodJohn H. HaltonJohn H. Haltonhttps://doi.org/10.1137/1012001PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] B. V. Gnedenko, The Theory of Probability, Chelsea, New York, 1962 Google Scholar[2] A. S. Frolov and , N. N. Chentsov, Use of dependent tests in the Monte Carlo method for obtaining smooth curves, Proc. Sixth All-Union Conf. Theory Prob. and Math. Statist. (Vilnius, 1960) (Russian), Gosudarstv. Izdat. Politi cesk. i Naučn. Lit. Litovsk. SSR, Vilnius, 1962, 425–437 MR0196902 Google Scholar[3] J. H. Halton, A general formulation of the Monte Carlo method and "strong laws" for certain sequential schemes, MRC Tech. Summary Rep., 690, Mathematics Research Center, University of Wisconsin, Madison, 1966 Google Scholar[4] John H. Halton, A retrospective and prospective survey of the Monte Carlo method, SIAM Rev., 12 (1970), 1–63 10.1137/1012001 MR0258231 0193.46901 LinkISIGoogle Scholar[5] J. H. Halton, Masters Thesis, Studies in the theory of the Monte Carlo method, Doctoral thesis, Oxford University, 1960 Google Scholar[6] J. H. Halton, Sequential Monte Carlo, Proc. Cambridge Philos. Soc., 58 (1962), 57–78, revised in [78] MR0140173 0119.14904 CrossrefISIGoogle Scholar[7] William J. Pervin, Foundations of general topology, Academic Press Textbooks in Mathematics, Academic Press, New York, 1964xi+209 MR0165477 0117.39701 Google Scholar[8] W. Sierpinski, General Topology, University of Toronto Press, Toronto, Ontario, 1956 Google Scholar[9] J. H. Halton, On the generation of random sequences in Fréchet spaces, Rep., AMD 374/BNL 8996, Brookhaven National Laboratory, Upton, N.Y., 1965, reprinted in [4] Google Scholar[10] J. F. Koksma, A general theorem from the theory of uniform distribution modulo 1, Mathematica, Zutphen. B., 11 (1942), 7–11, (In Dutch.) MR0015094 Google Scholar[11] J. P. Bertrandias, Calculation of an integral by means of the sequence $X_{n}=An$. Evaluation of the error, Publ. Inst. Statist. Univ. Paris, 9 (1960), 335–357 Google Scholar[12] C. B. Haselgrove, A method for numerical integration, Math. Comp., 15 (1961), 323–337 MR0146960 0209.46902 CrossrefGoogle Scholar[13] E. Hlawka, Functions of bounded variation in the theory of uniform distribution, Ann. Mat. Pura Appl., IV, 54 (1961), 325–334, (In German.) CrossrefGoogle Scholar[14] E. Hlawka, On the approximate computation of multiple integrals, Monatsh. Math., 66 (1962), 140–151 CrossrefGoogle Scholar[15] S. K. Zaremba, Good lattice points, discrepancy, and numerical integration, Ann. Mat. Pura Appl. [4], 73 (1966), 293–317 MR0218018 CrossrefGoogle Scholar[16] J. M. Hammersley and , K. W. Morton, Discussion, R. S. S. symposium on Monte Carlo methods, J. Roy. Statist. Soc. Ser. B, 16 (1954), 61–75, reprinted in [4] Google Scholar[17] J. M. Hammersley and , D. C. Handscomb, Monte Carlo methods, Methuen & Co. Ltd., London, 1965vii+178 MR0223065 0121.35503 Google Scholar[18] John H. Curtiss, Sampling methods applied to differential and difference equations, Proceedings, Seminar on Scientific Computation, November, 1949, International Business Machines Corp., New York, N. Y., 1950, 87–109, reprinted in [4] MR0043564 Google Scholar[19] Lord Rayleigh, On James Bernoulli's theorem in probabilities, Philos. Mag., 47 (1899), 246–251 CrossrefGoogle Scholar[20] "Student", Probable error of a correlation coefficient, Biometrika, 6 (1908), 302–310 CrossrefGoogle Scholar[21] R. Courant, , K. O. Friedrichs and , H. Lewy, On the partial difference equations of mathematical physics, Math. Ann., 100 (1928), 32–74, English transl., Courant Institute of Mathematical Sciences, New York University, 1956 CrossrefGoogle Scholar[22] A. N. Kolmogorov, On the analytic method in probability theory, Math. Ann., 104 (1931), 415–458 CrossrefGoogle Scholar[23] G. Pólya, On a random walk in a network of streets, Colloque consacré à la théorie des probabilités. I: Conférences d'introduction, Actualités scientifiques et industrielles, no. 734, Hermann, Paris, 1938, 25–44 Google Scholar[24] Nicholas Metropolis and , S. Ulam, The Monte Carlo method, J. Amer. Statist. Assoc., 44 (1949), 335–341, reprinted in [4] MR0031341 0033.28807 CrossrefISIGoogle Scholar[25] S. Ulam, On the Monte Carlo method, Proceedings of a Second Symposium on Large-Scale Digital Calculating Machinery, 1949, Harvard University Press, Cambridge, Mass., 1951, 207–212, reprinted in [4] MR0044897 Google Scholar[26] G. W. King, The Monte Carlo method as a natural mode of expression in operations research, J. Operations Res. Soc. Amer., 1 (1953), 46–51, reprinted in [4] CrossrefISIGoogle Scholar[27] J. M. Hammersley and , K. W. Morton, Poor man's Monte Carlo, J. Roy. Statist. Soc. Ser. B., 16 (1954), 23–38; discussion 61–75, reprinted in [4] MR0064475 0055.36901 Google Scholar[28] K. D. Tocher, The application of automatic computers to sampling experiments, J. Roy. Statist. Soc. Ser. B., 1