International Journal of Stochastic Analysis

International Journal of Stochastic Analysis / 1996 / Article

Open Access

Volume 9 |Article ID 953087 | 16 pages | https://doi.org/10.1155/S1048953396000354

A probabilistic approach to the trace at the boundary for solutions of a semilinear parabolic partial differential equation

Received01 Aug 1996
Revised01 Oct 1996

Abstract

We use the path-valued process called the “Brownian snake” to investigate the trace at the boundary of nonnegative solutions of a semilinear parabolic partial differential equation. In particular, we characterize possible traces and in dimension one we prove that nonnegative solutions are in one-to-one correspondence with their traces at the origin. We also provide probabilistic representations for various classes of solutions.This article is dedicated to the memory of Roland L. Dobrushin.

Copyright © 1996 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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