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A probabilistic approach to second order variational inequalities with bilateral constraints

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Abstract

We study a class of second order variational inequalities with bilateral constraints. Under certain conditions we show the existence of aunique viscosity solution of these variational inequalities and give a stochastic representation to this solution. As an application, we study a stochastic game with stopping times and show the existence of a saddle point equilibrium.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Science, 560 012, Bangalore, India

    Mrinal K. Ghosh

  2. Department of Electrical and Computer Engineering, University of Texas, TX 78712, Austin, USA

    Mrinal K. Ghosh

  3. CMI, Université de Provence, 39, Rue F. J. Curie, 13 453, Marseille, France

    K. S. Mallikarjuna Rao

Authors
  1. Mrinal K. Ghosh
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  2. K. S. Mallikarjuna Rao
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Correspondence to Mrinal K. Ghosh.

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Ghosh, M.K., Rao, K.S.M. A probabilistic approach to second order variational inequalities with bilateral constraints. Proc. Indian Acad. Sci. (Math. Sci.) 113, 431–442 (2003). https://doi.org/10.1007/BF02829634

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  • DOI: https://doi.org/10.1007/BF02829634

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