Calculation of Probability of the Exit of a Stochastic Process from a Band by Monte-Carlo Method: A Wiener-Hopf Factorization

Abstract

This paper considers a method of the calculation of probability of the exit from a band of the solution of a stochastic differential equation. The method is based on the approximation of the solution of the considered equation by a process which is received as a concatenation of Gauss processes, random partition of the interval, Girsanov transform and Wiener-Hopf factorization, and the Monte-Carlo method. The errors of approximation are estimated. The proposed method is illustrated by numerical examples.

Keywords

• Girsanov transform
• Monte-Carlo method
• probability of the exit from a band
• stochastic processes
• Wiener-Hopf factorization