Infinite dimensional weak Dirichlet processes and convolution type processes

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• 关键词：60H05 ; 60H15 ; 60H30 ; 35R60
• 刊名：Stochastic Processes and their Applications
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：127
• 期：1
• 页码：325-357
• 全文大小：459 K
• 卷排序：127

文摘

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 XX, taking values in a Banach space HH, 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))f(t,X(t)) where f:[0,T]×H→Rf:[0,T]×H→R is a C0,1C0,1 function and XX a convolution type process.