Mathematical Society of Japan Memoirs

Monte Carlo Method, Random Number, and Pseudorandom Number

Hiroshi Sugita

Book information

Hiroshi Sugita

Publication information
MSJ Memoirs, Volume 25
Tokyo, Japan: The Mathematical Society of Japan, 2011
133 pp.

Publication date: 2011
First available in Project Euclid: 11 December 2014

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Zentralblatt MATH:

Mathematical Reviews (MathSciNet):

Primary: 60-02: Research exposition (monographs, survey articles) 56-02
Secondary: 11K45: Pseudo-random numbers; Monte Carlo methods 65C05: Monte Carlo methods 65C10: Random number generation 68Q30: Algorithmic information theory (Kolmogorov complexity, etc.) [See also 03D32]

Copyright © 2011, The Mathematical Society of Japan

Hiroshi Sugita, Monte Carlo Method, Random Number, and Pseudorandom Number (Tokyo: The Mathematical Society of Japan, 2011)

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Although the Monte Carlo method is used in so many fields, its mathematical foundation has been weak until now because of the fundamental problem that a computer cannot generate random numbers. This book presents a strong mathematical formulation of the Monte Carlo method which is based on the theory of random number by Kolmogorov and others and that of pseudorandom number by Blum and others. As a result, we see that the Monte Carlo method may not need random numbers and pseudorandom numbers may suffice. In particular, for the Monte Carlo integration, there exist pseudorandom numbers which serve as complete substitutes for random numbers.