Monte Carlo methods

Monte Carlo and quasi-Monte Carlo methods

Monte Carlo is one of the most versatile and widely used numerical methods. Its convergence rate, O(N~^), is independent of dimension, which shows Monte Carlo to be very robust but also slow. This article presents an introduction to Monte Carlo methods for integration problems, including convergence theory, sampling methods and variance reduction techniques. Accelerated convergence for Monte Ca...

Parallel Monte Carlo Methods

This paper is the key paper in my Survey-based term project. The author argues that Monte Carlo algorithms are ideally suited to parallel computing, and that “parallel Monte Carlo” should be more widely used. Therefore I consider many of issues can be raised by use Parallel Monte Carlo method. And from this paper I also can discuss the possibilities of parallel Markov chain Monte Carlo which is...

Monte Carlo Methods

This tutorial describes numerical methods that are known as Monte Carlo methods. It starts with a basic description of the principles of Monte Carlo methods. It then discusses four individual Monte Carlo methods, describing each individual method and illustrating their use in calculating an integral. These four methods have been implemented in my example program 8.2, and the results from these ...

Multilevel Monte Carlo Methods

We study Monte Carlo approximations to high dimensional parameter dependent integrals. We survey the multilevel variance reduction technique introduced by the author in [4] and present extensions and new developments of it. The tools needed for the convergence analysis of vector-valued Monte Carlo methods are discussed, as well. Applications to stochastic solution of integral equations are give...

Monte Carlo Methods