A Probabilistic Representation for the Solution of One Problem of Mathematical Physics
- Cite this article as:
- Portenko, N.I. Ukrainian Mathematical Journal (2000) 52: 1457. doi:10.1023/A:1010388321016
- 34 Views
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.