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Stochastic variational inequalities of parabolic type

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Abstract

Existence and uniqueness of strong solutions of stochastic partial differential equations of parabolic type with reflection (e.g., the solutions are never allowed to be negative) is proved. The problem is formulated as a stochastic variational inequality and then compactness is used to derive the result, but the method requires the space dimension to be one.

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Authors and Affiliations

  1. Mathematics Department, University of British Columbia, 121-1984 Mathematics Road, V6T 1Y4, Vancouver, B.C., Canada

    U. G. Haussmann

  2. Mathématiques—case H, Université de Provence, 13331, Marseille Cedex 3, France

    E. Pardoux

Authors
  1. U. G. Haussmann
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  2. E. Pardoux
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Additional information

Communicated by A. Bensoussan

This research was supported by NSERC under Grant No. 8051.

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Haussmann, U.G., Pardoux, E. Stochastic variational inequalities of parabolic type. Appl Math Optim 20, 163–192 (1989). https://doi.org/10.1007/BF01447653

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  • DOI: https://doi.org/10.1007/BF01447653

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