A Probabilistic Representation for the Solution of One Problem of Mathematical Physics

Authors

  • N. I. Portenko

Abstract

We consider a multidimensional Wiener process with a semipermeable membrane located on a given hyperplane. The paths of this process are the solutions of a stochastic differential equation, which can be regarded as a generalization of the well-known Skorokhod equation for a diffusion process in a bounded domain with boundary conditions on the boundary. We randomly change the time in this process by using an additive functional of the local-time type. As a result, we obtain a probabilistic representation for solutions of one problem of mathematical physics.

Published

25.09.2000

Issue

Section

Research articles

How to Cite

Portenko, N. I. “A Probabilistic Representation for the Solution of One Problem of Mathematical Physics”. Ukrains’kyi Matematychnyi Zhurnal, vol. 52, no. 9, Sept. 2000, pp. 1272-8, https://umj.imath.kiev.ua/index.php/umj/article/view/4534.