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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Bibliographic Details
Published in:Stochastic processes and their applications Vol. 127; no. 1; pp. 325 - 357
Main Authors: Fabbri, Giorgio, Russo, Francesco
Format: Journal Article
Language:English
Published: Elsevier 01.01.2017
Subjects:
Economics and Finance
Humanities and Social Sciences
Mathematics
tensor analysis
calculus via regularization
convolution type processes
stochastic partial differential equations
Dirichlet processes
generalized Fukushima decomposition
infinite dimensional analysis
covariation and quadratic variation
ISSN:0304-4149, 1879-209X
Online Access:Get full text
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Summary: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 to f(t, X(t)) where f : [0, T ] × H → R is a C0,1 function and X a convolution type processes.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2016.06.010