On a new probabilistic representation for the solution of the heat equation

Paolo Da Pelo; Alberto Lanconelli

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arXiv · 1002.4269

On a new probabilistic representation for the solution of the heat equation

Paolo Da Pelo·Alberto Lanconelli

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Abstract

We obtain a new probabilistic representation for the solution of the heat equation in terms of a product for smooth random variables which is introduced and studied in this paper. This multiplication, expressed in terms of the Hida-Malliavin derivatives of the random variables involved, exhibits many useful properties which are to some extents opposite to some peculiar features of the Wick product.

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Paolo Da Pelo, Alberto Lanconelli. 2010-02-23. On a new probabilistic representation for the solution of the heat equation. https://arxiv.org/abs/1002.4269

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