Infinite dimensional weak Dirichlet processes and convolution type processes

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:127

Article

Fabbri, Giorgio^1,2  Russo, Francesco³ 

[1] Aix Marseille Univ, Aix Marseille Sch Econ, CNRS, 2 Rue Charite, F-13002 Marseille, France

[2] EHESS, Ctr Vieille Charite, 2 Rue Charite, F-13002 Marseille, France

[3] Univ Paris Saclay, ENSTA ParisTech, Unite Math Appl, 828 Blvd Marechaux, F-91120 Palaiseau, France

关键词: Covariation and quadratic variation;    Calculus via regularization;    Infinite dimensional analysis;    Tensor analysis;    Dirichlet processes;    Generalized Fukushima decomposition;    Convolution type processes;    Stochastic partial differential equations;   

DOI  :  10.1016/j.spa.2016.06.010

来源: Elsevier

【 摘 要 】

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 Ito's type formula applied to f (t, X(t)) where f : [0, 7] x H -> R is a C-0,C-1 function and X a convolution type process. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

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