Article2004

Uniqueness for stochastic evolution equations in Banach spaces

179 citations0/0 files storedDissertationes Mathematicae

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Stochastic processes and financial applications Nonlinear Differential Equations Analysis Differential Equations and Boundary Problems

Abstract

Different types of uniqueness (e.g. pathwise uniqueness, uniqueness in law, joint uniqueness in law) and existence (e.g. strong solution, martingale solution) for stochastic evolution equations driven by a Wiener process are studied and compared. We show

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1991Continuous Martingales and Brownian Motion 1989Brownian Motion and Stochastic Calculus.1971On the uniqueness of solutions of stochastic differential equations

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2008Yamada-Watanabe theorem for stochastic evolution equations in infinite dimensions 2008Maximal regularity for stochastic convolutions driven by Lévy processes 2013Stochastic geometric wave equations with values in compact Riemannian homogeneous spaces 2005Brownian Representations of Cylindrical Local Martingales, Martingale Problem and Strong Markov Property of Weak Solutions of SPDEs in Banach Spaces 2015Gradient estimates and applications for SDEs in Hilbert space with multiplicative noise and Dini continuous drift 2015Yamada-Watanabe Results for Stochastic Differential Equations with Jumps 2014Strong Uniqueness for Stochastic Evolution Equations with Unbounded Measurable Drift Term 2013The covariation for Banach space valued processes and applications

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