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    • Probabilistic representations of solutions to the heat equation

      B Rajeev S Thangavelu

      Volume 113 Issue 3 August 2003 pp 321-332

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/113/03/0321-0332

    • Keywords

       

      Brownian motion; heat equation; translation operators; infinite dimensional stochastic differential equations

    • Abstract

       

      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.

    • Author Affiliations

       

      B Rajeev1 S Thangavelu1

      1. Indian Statistical Institute, R.V. College Post, Bangalore - 560 059, India

    • Dates

       
      Published
      August 2003
      Manuscript received
      16 November 2002

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