Infinite Dimensional Weak Dirichlet Processes and Convolution Type Processes

Giorgio Fabbri and Francesco Russo ()
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Francesco Russo: OC - Optimisation et commande - UMA - Unité de Mathématiques Appliquées - ENSTA Paris - École Nationale Supérieure de Techniques Avancées - IP Paris - Institut Polytechnique de Paris

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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 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.

Keywords: infinite dimensional analysis; calculus via regularization; covariation and quadratic variation; Dirichlet processes; tensor analysis; generalized Fukushima decomposition; convolution type processes; stochastic partial differential equations (search for similar items in EconPapers)
Date: 2017-01
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01309384v1
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Published in Stochastic Processes and their Applications, 2017, 127 (1), pp.325-357. ⟨10.1016/j.spa.2016.06.010⟩

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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 (2016)
Working Paper: Infinite dimensional weak Dirichlet processes and convolution type processes (2016)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-01309384

DOI: 10.1016/j.spa.2016.06.010

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