期刊论文详细信息
Proceedings Mathematical Sciences | |
Probabilistic Representations of Solutions to the Heat Equation | |
B Rajeev2  S Thangavelu1  | |
[1] $$;Indian Statistical Institute, R.V. College Post, Bangalore 0 0, India$$ | |
关键词: Brownian motion; heat equation; translation operators; infinite dimensional stochastic differential equations.; | |
DOI : | |
学科分类:数学(综合) | |
来源: Indian Academy of Sciences | |
【 摘 要 】
In this paper we provide a new (probabilistic) proof of a classical result in partial differential equations, viz. if 𜙠is a tempered distribution, then the solution of the heat equation for the Laplacian, with initial condition ðœ™, is given by the convolution of 𜙠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.
【 授权许可】
Unknown
【 预 览 】
Files | Size | Format | View |
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RO201912040506623ZK.pdf | 104KB | download |