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

Grigory Beliavsky, Natalya Danilova and Guennady Ougolnitsky
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Grigory Beliavsky: Vorovich Institute of Mathematics, Mechanics and Computer Sciences, Southern Federal University, 8A Milchakov St., Rostov-on-Don 344090, Russia
Natalya Danilova: Vorovich Institute of Mathematics, Mechanics and Computer Sciences, Southern Federal University, 8A Milchakov St., Rostov-on-Don 344090, Russia
Guennady Ougolnitsky: Vorovich Institute of Mathematics, Mechanics and Computer Sciences, Southern Federal University, 8A Milchakov St., Rostov-on-Don 344090, Russia

Mathematics, 2019, vol. 7, issue 7, 1-8

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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