Monte Carlo Methods

Simulations of Stochastic Systems: Radiation Transport and Monte Carlo Evaluation of Finite-Dimensional Integrals show random walks, Integral Equations, and Variance Reduction in addition to classical Monte Carlo methods.

Abstract

This introduction to Monte Carlo Methods seeks to identify and study the unifying elements that underlie their effective application. It focuses on two basic themes. The first is the importance of random walks as they occur both in natural stochastic systems and in their relationship to integral and differential equations. The second theme is that of variance reduction in general and importance sampling in particular as a technique for efficient use of the methods. Random walks are introduced with an elementary example in which the modelling of radiation transport arises directly from a schematic probabilistic description of the interaction of radiation with matter