A Probabilistic Representation for the Solution of One Problem of Mathematical Physics |
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Authors: | Portenko N I |
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Institution: | (1) Institute of Mathematics, Ukrainian Academy of Sciences, Kiev |
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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. |
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