Stochastic variational inequalities with oblique subgradients

Anouar M. Gassous, Aurel Răşcanu and Eduard Rotenstein

Stochastic Processes and their Applications, 2012, vol. 122, issue 7, 2668-2700

Abstract: In this paper we will study the existence and uniqueness of the solution for the stochastic variational inequality with oblique subgradients of the following form: {dXt+H(Xt)∂φ(Xt)(dt)∋f(t,Xt)dt+g(t,Xt)dBt,t>0,X0=x∈Dom(φ)¯. Here, the mixture between the monotonicity property of the subdifferential operator ∂φ and the Lipschitz property of the matrix mapping X⟼H(X) leads to stronger difficulties in comparison to the classical case of stochastic variational inequalities. The existence result is based on a deterministic approach: a differential system with singular input is first analyzed.

Keywords: Oblique reflection; Skorohod problem; Stochastic variational inequalities (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spa.2012.04.012

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