GENERALIZED COVARIATION AND EXTENDED FUKUSHIMA DECOMPOSITION FOR BANACH SPACE-VALUED PROCESSES: APPLICATIONS TO WINDOWS OF DIRICHLET PROCESSES

DOI10.1142/S0219025712500075zbMath1279.60067arXiv1105.4419MaRDI QIDQ2909256

Francesco Russo, Cristina Di Girolami

Publication date: 30 August 2012

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.4419

zbMATH Keywords

Malliavin calculusDirichlet processestensor analysisgeneralized Fukushima decompositioninfinite-dimensional analysiscalculus via regularizationcovariation and quadratic variationrepresentation of path-dependent random variables

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Applications of stochastic analysis (to PDEs, etc.) (60H30) Financial applications of other theories (91G80) Stochastic integrals (60H05) Stochastic calculus of variations and the Malliavin calculus (60H07)

Related Items (11)

An infinite-dimensional approach to path-dependent Kolmogorov equations ⋮ Infinite dimensional weak Dirichlet processes and convolution type processes ⋮ Infinite-dimensional calculus under weak spatial regularity of the processes ⋮ Cylindrical fractional Brownian motion in Banach spaces ⋮ Functional Itô versus Banach space stochastic calculus and strict solutions of semilinear path-dependent equations ⋮ HJB Equations in Infinite Dimension and Optimal Control of Stochastic Evolution Equations Via Generalized Fukushima Decomposition ⋮ The covariation for Banach space valued processes and applications ⋮ Stochastic systems with memory and jumps ⋮ Path-dependent equations and viscosity solutions in infinite dimension ⋮ Calculus via regularizations in Banach spaces and Kolmogorov-type path-dependent equations ⋮ Crandall-Lions viscosity solutions for path-dependent PDEs: the case of heat equation

Cites Work

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• Les processus de dirichlet et tant qu'espace de banach
• Covariation de convolution de martingales
• Stochastic calculus with respect to continuous finite quadratic variation processes
• Generalized calculus and sdes with non regular drift
• A generalized class of Lyons-Zheng processes

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