Probabilistic representations of solutions to the heat equation

被引：0
作者：
B. Rajeev
S. Thangavelu
机构：
[1] Indian Statistical Institute,
来源：
Proceedings of the Indian Academy of Sciences - Mathematical Sciences | 2003年 / 113卷
关键词：
Brownian motion; heat equation; translation operators; infinite dimensional stochastic differential equations;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper we provide a new (probabilistic) proof of a classical result in partial differential equations, viz. if ϕ is a tempered distribution, then the solution of the heat equation for the Laplacian, with initial condition ϕ, is given by the convolution of ϕ with the heat kernel (Gaussian density). Our results also extend the probabilistic representation of solutions of the heat equation to initial conditions that are arbitrary tempered distributions.
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页码：321 / 332
页数：11
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