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Existence for a class of stochastic parabolic variational inequalities

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Stochastic processes and financial applications Nonlinear Partial Differential Equations Optimization and Variational Analysis

Abstract

In this paper we deal with the existence of a nonanticipative stochastic process M, solution of the stochastic parabolic variational inequality for all v and m in some fixed spaces of stochastic processes (m and M are martingales). If ϕ is a convex indicator function, we obtain a “maximal solution”.

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1976Stochastic Differential Equations and Applications 1980Stochastic partial differential equations and filtering of diffusion processes 2010Stochastic Differential Equations and Applications 1970Ito's lemma in infinite dimensions 1970Stochastic Integrals Based on Martingales Taking Values in Hilbert Space

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2015Backward stochastic variational inequalities on random interval

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