Probabilistic representations of solutions to the heat equation

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dc.creatorRajeev, B.
dc.creatorThangavelu, S.
dc.date2003-10-17
dc.date.accessioned2026-07-07T05:02:00Z
dc.date.available2026-07-07T05:02:00Z
dc.descriptionIn 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.
dc.description12 pages
dc.identifierhttps://arxiv.org/abs/math/0310262
dc.identifierhttp://arxiv.org/abs/math/0310262
dc.identifierProc. Indian Acad. Sci. (Math. Sci.), Vol. 113, No. 3, August 2003, pp. 321-332
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/68890
dc.subjectProbability
dc.subjectAnalysis of PDEs
dc.titleProbabilistic representations of solutions to the heat equation
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