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Ukrainian Mathematical Journal
, Volume 52, Issue 9, pp 14571469
A Probabilistic Representation for the Solution of One Problem of Mathematical Physics
 N. I. PortenkoAffiliated withInstitute of Mathematics, Ukrainian Academy of Sciences
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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 wellknown 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 localtime type. As a result, we obtain a probabilistic representation for solutions of one problem of mathematical physics.
 Title
 A Probabilistic Representation for the Solution of One Problem of Mathematical Physics
 Journal

Ukrainian Mathematical Journal
Volume 52, Issue 9 , pp 14571469
 Cover Date
 200009
 DOI
 10.1023/A:1010388321016
 Print ISSN
 00415995
 Online ISSN
 15739376
 Publisher
 Kluwer Academic PublishersPlenum Publishers
 Additional Links
 Authors

 N. I. Portenko ^{(1)}
 Author Affiliations

 1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev