Infinite Dimensional Weak Dirichlet Processes and Convolution Type Processes

Giorgio Fabbri and Francesco Russo ()
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Francesco Russo: ENSTA ParisTech, Université Paris-Saclay, Unité de Mathématiques appliquées

No 1616, AMSE Working Papers from Aix-Marseille School of Economics, France

Abstract: The present paper continues the study of infinite dimensional calculus via regularization, started by C. Di Girolami and the second named author, introducing the notion of weak Dirichlet process in this context. Such a process X, taking values in a Banach space H, is the sum of a local martingale and a suitableorthogonal process. The concept of weak Dirichlet process fits the notion of convolution type processes, a class including mild solutions for stochastic evolution equations on infinite dimensional Hilbert spaces and in particular of several classes of stochastic partial differential equations (SPDEs). In particular the mentioned decomposition appears to be a substitute of an Itô’s type formula applied to to f(t, X(t)) where f : [0, T ] × H ? R is a C0,1 function and X a convolution type processes.

Keywords: Covariation and Quadratic variation; Calculus via regularization; Infi- nite dimensional analysis; Tensor analysis; Dirichlet processes; Generalized Fukushima decomposition; Convolution type processes; Stochastic partial differential equations. (search for similar items in EconPapers)
Pages: 30 pages
Date: 2016-04-20, Revised 2016-04-20
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Related works:
Journal Article: Infinite dimensional weak Dirichlet processes and convolution type processes (2017)
Working Paper: Infinite Dimensional Weak Dirichlet Processes and Convolution Type Processes (2017)
Working Paper: Infinite dimensional weak Dirichlet processes and convolution type processes (2016)
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