Backward stochastic dynamics with a subdifferential operator and non-local parabolic variational inequalities

Alain Bensoussan, Yiqun Li and Sheung Chi Phillip Yam

Stochastic Processes and their Applications, 2018, vol. 128, issue 2, 644-688

Abstract: In this article, we provide the first systematic study on the unique existence of the solution of backward stochastic dynamical variational inequalities on a general complete filtered probability space. We also build up a comprehensive analysis of the correspondence between these stochastic variational inequalities (resp. backward stochastic dynamics) and the weak solutions (instead of viscosity ones due to the intrinsic non-local nature of the integral of the gradient involved) of a class of non-local parabolic variational inequalities (resp. parabolic partial differential equations), which is barely touched in the existing literature due to its unconventional setting.

Keywords: Backward stochastic dynamical variational inequalities; Integral of gradient; Non-local parabolic partial differential equations; Non-local parabolic variational inequalities; Norm equivalence; Penalized approach; Weak solutions (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:128:y:2018:i:2:p:644-688

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DOI: 10.1016/j.spa.2017.06.005

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