17. Applications to Differential Equations

  1. Dirk P. Kroese1,
  2. Thomas Taimre1 and
  3. Zdravko I. Botev2

Published Online: 20 SEP 2011

DOI: 10.1002/9781118014967.ch17

Handbook of Monte Carlo Methods

Handbook of Monte Carlo Methods

How to Cite

Kroese, D. P., Taimre, T. and Botev, Z. I. (2011) Applications to Differential Equations, in Handbook of Monte Carlo Methods, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118014967.ch17

Author Information

  1. 1

    University of Queensland

  2. 2

    Université de Montréal

Publication History

  1. Published Online: 20 SEP 2011
  2. Published Print: 28 FEB 2011

ISBN Information

Print ISBN: 9780470177938

Online ISBN: 9781118014967



  • diffusion process;
  • functional central limit theorem approximation;
  • Markov jump processes;
  • Monte Carlo simulation;
  • partial differential equations;
  • stochastic equations


This chapter highlights various connections between Monte Carlo simulation and differential equations. It first explains the relation between stochastic and partial differential equations. Then, the chapter looks at simulating transport processes and their connections to certain partial differential equations. It also examines the scaling of Markov jump processes, giving a functional law of large numbers that relates the process to the solution of a system of ordinary differential equations. In addition, a functional central limit theorem approximation is given in the form of an approximating diffusion process.

Controlled Vocabulary Terms

central limit theorem; diffusion process; Markov models; Monte Carlo methods