Stochastic integration of functions with values in a Banach space

Jan van Neerven · Lutz W. Weis

134 citations0/0 files storedStudia Mathematica

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Stochastic processes and financial applications Nonlinear Differential Equations Analysis Advanced Banach Space Theory

Abstract

Let $H$ be a separable real Hilbert space and let $E$ be a real Banach space. In this paper we construct a stochastic integral for certain operator-valued functions ${\mit\Phi}:(0,T)\to{\scr L}(H,E)$ with respect to a cylindrical Wiener process $\{W_H(t)\

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2007Stochastic integration in UMD Banach spaces 2008Itô's formula in UMD Banach spaces and regularity of solutions of the Zakai equation 2016Stochastic evolution equations with Volterra noise 2015Ornstein-Uhlenbeck Processes Driven by Cylindrical Lévy Processes 2005On the Stochastic Fubini Theorem in Infinite Dimensions 2009Malliavin calculus and decoupling inequalities in Banach spaces 2009Cylindrical Levy processes in Banach spaces 2008Stochastic integration for Lévy processes with values in Banach spaces

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