# Probabilistic representations of solutions to the heat equation

@article{Rajeev2003ProbabilisticRO, title={Probabilistic representations of solutions to the heat equation}, author={Bhaskaran Rajeev and Sundaram Thangavelu}, journal={Proceedings of the Indian Academy of Sciences - Mathematical Sciences}, year={2003}, volume={113}, pages={321-332} }

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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