Infinite dimensional weak Dirichlet processes and convolution type processes

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 an...

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Vydané v:	Stochastic processes and their applications Ročník 127; číslo 1; s. 325 - 357
Hlavní autori:	Fabbri, Giorgio, Russo, Francesco
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier B.V 01.01.2017 Elsevier
Predmet:	Calculus via regularization Convolution type processes Covariation and quadratic variation Dirichlet processes Generalized Fukushima decomposition Infinite dimensional analysis Mathematics Probability Stochastic partial differential equations Tensor analysis Generalized Fukushima decomposition Convolution type processes 35R60 Stochastic partial differential equations Calculus via regularization 60H30 Covariation and quadratic variation Tensor analysis Infinite dimensional analysis Dirichlet processes 60H05 60H15 Covariation and Quadratic variation
ISSN:	0304-4149, 1879-209X
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Popis
Shrnutí:	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 suitable orthogonal 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 f(t,X(t)) where f:[0,T]×H→R is a C0,1 function and X a convolution type process.
ISSN:	0304-4149 1879-209X
DOI:	10.1016/j.spa.2016.06.010