A probabilistic representation for the solution of one problem of mathematical physics

• Published in: Український математичний журнал
• Date: 2000
• ISSN: 1027-3190
• Main Author: Portenko, N.I.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2000
• Subjects: Статті
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/158027
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: A probabilistic representation for the solution of one problem of mathematical physics / N.I. Portenko // Український математичний журнал. — 2000. — Т. 52, № 9. — С. 1272—1282. — Бібліогр.: 18 назв. — англ.

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 bo...