## Bernoulli

• Bernoulli
• Volume 21, Number 2 (2015), 1166-1199.

### Backward stochastic variational inequalities on random interval

#### 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.

#### Article information

Source
Bernoulli Volume 21, Number 2 (2015), 1166-1199.

Dates
First available in Project Euclid: 21 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.bj/1429624974

Digital Object Identifier
doi:10.3150/14-BEJ601

Mathematical Reviews number (MathSciNet)
MR3338660

Zentralblatt MATH identifier
1332.60085

#### Citation

Maticiuc, Lucian; Răşcanu, Aurel. Backward stochastic variational inequalities on random interval. Bernoulli 21 (2015), no. 2, 1166--1199. doi:10.3150/14-BEJ601. https://projecteuclid.org/euclid.bj/1429624974.

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