Backward stochastic differential equations with subdifferential operator and related variational inequalities

doi:10.1016/S0304-4149(98)00030-1

Stochastic Processes and their Applications

Volume 76, Issue 2, 15 August 1998, Pages 191-215

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Abstract

The existence and uniqueness of the solution of a backward SDE, on a random (possibly infinite) time interval, involving a subdifferential operator is proved. We then obtain a probabilistic interpretation for the viscosity solution of some parabolic and elliptic variational inequalities.

Keywords

Backward stochastic equations

Subdifferential operators

Variational inequalities

Viscosity solutions

Probabilistic formulae for PDE

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¹: The work of this author was done during a visit to the University of Provence & INRIA, whose generous support is gratefully acknowledged.