Ukrainian Mathematical Journal

, Volume 52, Issue 9, pp 1457–1469

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

  • N. I. Portenko

DOI: 10.1023/A:1010388321016

Cite this article as:
Portenko, N.I. Ukrainian Mathematical Journal (2000) 52: 1457. doi:10.1023/A:1010388321016


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.

Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • N. I. Portenko
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev