A recursive integration method for approximate solution of stochastic differential equations

Abstract

A deterministic approach for solving stochastic differential equations is described and numerically tested. In this approach, probability distributions of the sample paths at successive time steps in a numerical procedure are shown to satisfy a recursive integral equation. These probability distributions are approximated by solving the integral equation numerically. The advantage of this approach is the elimination of the need for computing sample paths of the solutions. This approach is useful, for example, in approximating the solution of first-passage time problems.

Keywords:

• Stochastic differential equations
• numerical analysis
• extrapolation
• first-passage time

C.R. Categories:

• G.1.1
• G.1.9
• G.3