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Stochastic variational inequalities with oblique subgradients


  • Gassous, Anouar M.
  • Răşcanu, Aurel
  • Rotenstein, Eduard


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.

Suggested Citation

  • Gassous, Anouar M. & Răşcanu, Aurel & Rotenstein, Eduard, 2012. "Stochastic variational inequalities with oblique subgradients," Stochastic Processes and their Applications, Elsevier, vol. 122(7), pages 2668-2700.
  • Handle: RePEc:eee:spapps:v:122:y:2012:i:7:p:2668-2700 DOI: 10.1016/

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    References listed on IDEAS

    1. Rozkosz, Andrzej & Slominski, Leszek, 1997. "On stability and existence of solutions of SDEs with reflection at the boundary," Stochastic Processes and their Applications, Elsevier, vol. 68(2), pages 285-302, June.
    2. Ramasubramanian, S., 2006. "An insurance network: Nash equilibrium," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 374-390, April.
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    Cited by:

    1. Zălinescu, Adrian, 2014. "Stochastic variational inequalities with jumps," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 785-811.
    2. Gassous, Anouar M. & Răşcanu, Aurel & Rotenstein, Eduard, 2015. "Multivalued backward stochastic differential equations with oblique subgradients," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 3170-3195.


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