Monte Carlo Methods, 2nd Edition

This introduction to Monte Carlo Methods seeks to identify and study the unifying elements that underlie their effective application. The book 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. Building on that example, the relationship between random walks and integral equations is outlined. The applicability of these ideas to other problems is shown by a clear and elementary introduction to the solution of the Schrodinger equation by random walks.

This is the second, completely revised and extended edition of the successful monograph which brings the treatment up to date while retaining its elementary but general approach.