Monte-Carlo Methods and Stochastic Processes

From Linear to Non-Linear

Emmanuel Gobet

• Publisher: Chapman and Hall/CRC
• Year: 2016
• ISBN:
  9781498746250
• Edition: 1
• Topic: Matematica
• Subtopic: Probabilità e statistica

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.

Table of contents

• Cover
• Half Title
• Title
• Copyright
• Dedication
• Contents
• Preface
• List of Figures
• List of Algorithms
• INTRODUCTION: BRIEF OVERVIEW OF MONTE-CARLO METHODS
• PART A: TOOLBOX FOR STOCHASTIC SIMULATION
• PART B: SIMULATION OF LINEAR PROCESSES
• PART C: SIMULATION OF NON-LINEAR PROCESSES
• Appendix A: Reminders and complementary results
• Bibliography
• Index