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2013 | OriginalPaper | Chapter

2. Strong Law of Large Numbers and Monte Carlo Methods

Authors : Carl Graham, Denis Talay

Published in: Stochastic Simulation and Monte Carlo Methods

Publisher: Springer Berlin Heidelberg

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Abstract

The principles of Monte Carlo methods based on the Strong Law of Large Numbers (SLLN) are detailed. A number of examples are described, some of which correspond to concrete problems in important application fields. This is followed by the discussion and description of various algorithms of simulation, first for uniform random variables, then using these for general random variables. Eventually, the more advanced topic of martingale theory is introduced, and the SLLN is proved using a backward martingale technique and the Kolmogorov zero-one law.

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previous chapter Introduction
next chapter Non-asymptotic Error Estimates for Monte Carlo Methods
Footnotes
1
This means that there exists a low complexity algorithm for generating sequences of independent samples from their common probability distribution.
 
2
This result is originally due to M. Greenberger, “Notes on a new pseudo-random number generator”, J. Assoc. Comput. Mach. 8, 163–167 (1961).
 
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Metadata
Title
Strong Law of Large Numbers and Monte Carlo Methods
Authors
Carl Graham
Denis Talay
Copyright Year
2013
Publisher
Springer Berlin Heidelberg
Book
Stochastic Simulation and Monte Carlo Methods

Print ISBN: 978-3-642-39362-4

Electronic ISBN: 978-3-642-39363-1

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-3-642-39363-1_2