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). A new probabilistic representation for the solution of the heat equation. STOCHASTICS, 84(2-3), 171-181 [10.1080/17442508.2011.616207].
A new probabilistic representation for the solution of the heat equation
Lanconelli A
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 productFile in questo prodotto:
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