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}
}
  • B. RajeevS. Thangavelu
  • Published 1 August 2003
  • Mathematics
  • Proceedings of the Indian Academy of Sciences - Mathematical Sciences
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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