Standard Article

Diffusion Processes

Probability Theory

  1. Michael Sørensen

Published Online: 15 SEP 2006

DOI: 10.1002/9780470012505.tad022

Encyclopedia of Actuarial Science

Encyclopedia of Actuarial Science

How to Cite

Sørensen, M. 2006. Diffusion Processes. Encyclopedia of Actuarial Science. 1.

Author Information

  1. University of Copenhagen, Department of Applied Mathematics and Statistics, Denmark

Publication History

  1. Published Online: 15 SEP 2006


Diffusion processes form stochastic models for a number of quantities familiar within an actuarial context. Derivative pricing, volatility and interest rates are but a few examples. Moreover, many processes in actuarial science such as the surplus process, can be conveniently approximated by diffusion processes. This article explains the most important concepts needed to describe diffusion processes. It further provides a number of models that have proved their applicability within a financial context such as Brownian motion, Ornstein-Uhlenbeck and Cox-Ingersoll-Ross.


  • central limit theorem;
  • ergodicity;
  • scale measure;
  • speed measure;
  • statistical inference;
  • stochastic differential equation;
  • transition density