5. Random Process Generation

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

Published Online: 20 SEP 2011

DOI: 10.1002/9781118014967.ch5

Handbook of Monte Carlo Methods

Handbook of Monte Carlo Methods

How to Cite

Kroese, D. P., Taimre, T. and Botev, Z. I. (2011) Random Process Generation, in Handbook of Monte Carlo Methods, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118014967.ch5

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

SEARCH

Keywords:

  • Brownian bridge;
  • diffusion process;
  • fractional Brownian motion;
  • Gaussian process;
  • geometric Brownian motion;
  • Markov chain;
  • Monte Carlo simulation;
  • Ornstein-Uhlenbeck process;
  • Poisson process;
  • random process generation

Summary

This chapter lists the major random processes used in Monte Carlo simulation, along with their main properties and how to generate them. It describes the Gaussian processes, Markov chains, Markov jump processes, Poisson processes, Wiener process (Brownian motion), and stochastic differential equations (SDEs) and diffusion processes. The chapter also discusses three general techniques for approximately simulating diffusion processes, and one less general technique for exactly simulating certain diffusion processes. The approximate methods discussed are the direct Euler method, Milstein's method, and the implicit Euler method. The exact method is due to Beskos and Roberts. Further, the chapter includes information about the Brownian bridge, Ornstein-Uhlenbeck process, reflected Brownian motion, Geometric Brownian motion, and Fractional Brownian motion, random fields, Levy processes, and time series.

Controlled Vocabulary Terms

Brownian bridge; diffusion process; fractional Brownian motion; Gaussian process; geometric Brownian motion; Markov chain; Monte Carlo methods; Ornstein-Uhlenbeck process; Poisson process