Monte Carlo methods (general)
RAND Corporation, A Million Random Digits with 100,000 Normal Deviates, Free Press, 1955. [link]
J. M. Hammersley and D. C. Handscomb, Monte Carlo Methods, Chapman and Hall, 1964. [doi]
L. Devroye, Non-Uniform Random Variate Generation, Springer, 1986. [doi]
P. Glasserman, Monte Carlo Methods in Financial Engineering, Springer, 2003. [doi]
D. P. Kroese, T. Taimre, and Z. I. Botev, Handbook of Monte Carlo Methods, John Wiley & Sons, 2011. [doi]
（和訳本）伏見 正則, 逆瀬川 浩孝（監訳）, モンテカルロ法ハンドブック, 朝倉書店, 2014. [link]
A. B. Owen, Monte Carlo Theory, Methods and Examples, 2013. [link]
鈴木 航介, 合田 隆. 重点解説 モンテカルロ法と準モンテカルロ法, サイエンス社, SGCライブラリ, 2025. [link]
Quasi-Monte Carlo methods and uniform distribution theory
L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences, Dover Publications, 1974. [link]
H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, SIAM, 1992. [doi] [link]
I. H. Sloan and S. Joe, Lattice Methods for Multiple Integration, Oxford University Press, 1994. [doi]
S. Tezuka, Uniform Random Numbers: Theory and Practice, Kluwer Academic Publishers, 1995. [doi]
M. Drmota and R. F. Tichy, Sequences, Discrepancies and Applications, Springer, 1997. [doi]
J. Matousek, Geometric Discrepancy: An Illustrated Guide, Springer, 1999. [doi]
C. Lemieux, Monte Carlo and Quasi-Monte Carlo Sampling, Springer, 2009. [doi]
J. Dick and F. Pillichshammer, Digital Nets and Sequences: Discrepancy Theory and Quasi–Monte Carlo Integration, Cambridge University Press, 2010. [doi] [link]
G. Leobacher and F. Pillichshammer, Introduction to Quasi-Monte Carlo Integration and Applications, Birkhauser, 2014. [doi]
J. Dick, P. Kritzer, and F. Pillichshammer, Lattice Rules: Numerical Integration, Approximation, and Discrepancy, Springer, 2022. [doi]
鈴木 航介, 合田 隆. 重点解説 モンテカルロ法と準モンテカルロ法, サイエンス社, SGCライブラリ, 2025. [link]
Markov chain Monte Carlo methods
C. P. Robert and G. Casella, Monte Carlo Statistical Methods, Springer, 1999. [doi]
J. S. Liu, Monte Carlo Strategies in Scientific Computing, Springer, 2004. [doi]
鎌谷研吾. モンテカルロ統計計算, 講談社, データサイエンス入門シリーズ, 2020. [link]
Others
P. J. Davis and P. Rabinowitz, Methods of Numerical Integration, Academic Press, 1984. [link]
E. Novak, Deterministic and Stochastic Error Bounds in Numerical Analysis, Springer, 1988. [doi]
K.-T. Fang, R. Li, and A. Sudjianto, Design and Modeling for Computer Experiments, Chapman and Hall/CRC, 2005. [doi]
S. Asmussen and P. W. Glynn, Stochastic Simulation: Algorithms and Analysis, Springer, 2007. [doi]
A. Saltelli, M. Ratto, T. Andres, F. Campolongo, J. Cariboni, D. Gatelli, M. Saisana, and S. Tarantola, Global Sensitivity Analysis. The Primer, John Wiley & Sons, 2008. [doi]
E. Novak and H. Woźniakowski, Tractability of Multivariate Problems: Volume I. Linear Information, EMS Press, 2008. [doi]
E. Novak and H. Woźniakowski, Tractability of Multivariate Problems: Volume II. Standard Information for Functionals, EMS Press, 2010. [doi]
E. Novak and H. Woźniakowski, Tractability of Multivariate Problems: Volume III. Standard Information for Operators, EMS Press, 2012. [doi]
K. Law, A. Stuart, and K. Zygalakis, Data Assimilation: A Mathematical Introduction, Springer, 2015. [doi]
T. J. Sullivan, Introduction to Uncertainty Quantification, Springer, 2015. [doi]
T. J. Santner, B. J. Williams, and W. I. Notz, The Design and Analysis of Computer Experiments, Springer, 2018. [doi]
N. Chopin and O. Papaspiliopoulos, An Introduction to Sequential Monte Carlo, Springer, 2020. [doi]
S. Da Veiga, F. Gamboa, B. Iooss, and C. Prieur, Basics and Trends in Sensitivity Analysis: Theory and Practice in R, SIAM, 2021. [doi]
R. E. Caflisch, Monte Carlo and quasi-Monte Carlo methods, Acta Numerica, 7:1-49, 1998. [doi]
P L’Ecuyer and C Lemieux, Recent advances in randomized quasi-Monte Carlo methods, in: Modeling Uncertainty: an Examination of Stochastic Theory, Methods, and Applications, pp. 419-474, 2002. [doi]
D. Bilyk, On Roth’s orthogonal function method in discrepancy theory, Uniform Distribution Theory, 6(1):143-184, 2011. [link]
J. Dick, F. Y. Kuo, and I. H. Sloan, High-dimensional integration: The quasi-Monte Carlo way, Acta Numerica, 22:133-288, 2013. [doi]
J. Dick, A. Hinrichs, and F. Pillichshammer, Proof techniques in quasi-Monte Carlo theory, Journal of Complexity, 31(3):327-371, 2015. [doi]
M. B. Giles, Multilevel Monte Carlo methods, Acta Numerica, 24:259-328, 2015. [doi]
T. Goda and K. Suzuki, Recent advances in higher order quasi-Monte Carlo methods, in: Discrepancy Theory, pp. 69-102, 2020. [doi]
鈴木 航介, 合田 隆. 準モンテカルロ法の最前線, 日本応用数理学会論文誌, 30(4):320-374, 2020. [doi]