A probabilistic representation for the solution of a problem of mathematical physics (Q2722158)
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scientific article; zbMATH DE number 1617399
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A probabilistic representation for the solution of a problem of mathematical physics |
scientific article; zbMATH DE number 1617399 |
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11 July 2001
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multidimensional Wiener process
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semipermeable membrane
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Skorokhod equation
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0.89269423
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0.89087754
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0.8899469
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0.8866451
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0.88594747
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0.87633574
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0.8751805
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A probabilistic representation for the solution of a problem of mathematical physics (English)
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This paper is devoted to the probabilistic representation of the solution of a problem of mathematical physics. A multidimensional Wiener process with a semipermeable membrane situated on a given hyperplane is considered. The paths of this process are solutions of a stochastic differential equation which can be regarded as a generalization of the well-known Skorokhod equation for diffusion process in a bounded domain with boundary conditions. The time in this process is randomly changed by using an additive functional of local time type. As a result, a probabilistic representation for solutions of some problems of mathematical physics is obtained.
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