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

2010/02/23 by Paolo Da Pelo, Da Pelo, Paolo, Alberto Lanconelli +1
Economics, Econometrics and Finance · Mathematics · #60H07 #60H30 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Statistical Research #Stochastic processes and financial applications #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1002.4269

openalex publication_date 2010/02/23 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We obtain a new probabilistic representation for the solution of the heat\nequation in terms of a product for smooth random variables which is introduced\nand studied in this paper. This multiplication, expressed in terms of the\nHida-Malliavin derivatives of the random variables involved, exhibits many\nuseful properties which are to some extents opposite to some peculiar features\nof the Wick product.\n

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