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 that are to some extents opposite to some peculiar features of the Wick product.
On a new probabilistic representation for the solution of the heat equation / da Pelo P.; Lanconelli A.. - In: STOCHASTICS. - ISSN 1744-2508. - STAMPA. - 84:2-3(2012), pp. 171-181. [10.1080/17442508.2011.616207]
On a new probabilistic representation for the solution of the heat equation
Lanconelli A.
Secondo
Investigation
2012
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 that are to some extents opposite to some peculiar features of the Wick product.File in questo prodotto:
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