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May 2015 Backward stochastic variational inequalities on random interval
Lucian Maticiuc, Aurel Răşcanu
Bernoulli 21(2): 1166-1199 (May 2015). DOI: 10.3150/14-BEJ601

Abstract

The aim of this paper is to study, in the infinite dimensional framework, the existence and uniqueness for the solution of the following multivalued generalized backward stochastic differential equation, considered on a random, possibly infinite, time interval:

\[\cases{-\mathrm{d}Y_{t}+\partial_{y}\Psi (t,Y_{t})\,\mathrm{d}Q_{t}\ni\Phi (t,Y_{t},Z_{t})\,\mathrm{d}Q_{t}-Z_{t}\,\mathrm{d}W_{t},\qquad0\leq t<\tau,\cr{Y_{\tau}=\eta,}}\] where $\tau$ is a stopping time, $Q$ is a progressively measurable increasing continuous stochastic process and $\partial_{y}\Psi$ is the subdifferential of the convex lower semicontinuous function $y\longmapsto\Psi (t,y)$.

As applications, we obtain from our main results applied for suitable convex functions, the existence for some backward stochastic partial differential equations with Dirichlet or Neumann boundary conditions.

Citation

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Lucian Maticiuc. Aurel Răşcanu. "Backward stochastic variational inequalities on random interval." Bernoulli 21 (2) 1166 - 1199, May 2015. https://doi.org/10.3150/14-BEJ601

Information

Published: May 2015
First available in Project Euclid: 21 April 2015

zbMATH: 1332.60085
MathSciNet: MR3338660
Digital Object Identifier: 10.3150/14-BEJ601

Rights: Copyright © 2015 Bernoulli Society for Mathematical Statistics and Probability

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Vol.21 • No. 2 • May 2015
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