Monte-Carlo Methods and Stochastic Processes: From Linear to Non-Linear

Emmanuel Gobet

August 1, 2016 by Chapman and Hall/CRC
Textbook - 310 Pages - 30 B/W Illustrations
ISBN 9781498746229 - CAT# K26985

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Features

  • Covers a broad spectrum of advanced and modern tools of probability, statistics, and PDEs, along with systematic computational concerns regarding numerical efficiency
  • Emphasizes the main algorithms and most important convergence phenomena
  • Encourages students to implement the algorithms to improve their own computational intuition
  • Presents simple proofs of results
  • Provides simulation exercises in Python on the author’s website

A solutions manual and figure slides are available upon qualifying course adoption.

Summary

Developed from the author’s course at the Ecole Polytechnique, Monte-Carlo Methods and Stochastic Processes: From Linear to Non-Linear focuses on the simulation of stochastic processes in continuous time and their link with partial differential equations (PDEs). It covers linear and nonlinear problems in biology, finance, geophysics, mechanics, chemistry, and other application areas. The text also thoroughly develops the problem of numerical integration and computation of expectation by the Monte-Carlo method.

The book begins with a history of Monte-Carlo methods and an overview of three typical Monte-Carlo problems: numerical integration and computation of expectation, simulation of complex distributions, and stochastic optimization. The remainder of the text is organized in three parts of progressive difficulty. The first part presents basic tools for stochastic simulation and analysis of algorithm convergence. The second part describes Monte-Carlo methods for the simulation of stochastic differential equations. The final part discusses the simulation of non-linear dynamics.