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.
da Pelo P., Lanconelli A. (2012). On a new probabilistic representation for the solution of the heat equation. STOCHASTICS, 84(2-3), 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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