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Stochastic Representation of Weak Solutions of Viscous Conservation Laws: A BSDE Approach

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  • Andrzej Rozkosz

    (Nicolaus Copernicus University)

Abstract

We consider the Cauchy problem for systems of viscous conservation laws. We obtain three different but related stochastic representations of weak solutions of the problem: in terms of solutions to systems of usual backward stochastic differential equations, in terms of solutions to some stochastic backward systems, and in terms of solutions to some forward-backward stochastic differential equations.

Suggested Citation

  • Andrzej Rozkosz, 2013. "Stochastic Representation of Weak Solutions of Viscous Conservation Laws: A BSDE Approach," Journal of Theoretical Probability, Springer, vol. 26(4), pages 1061-1083, December.
    • Handle: RePEc:spr:jotpro:v:26:y:2013:i:4:d:10.1007_s10959-011-0395-y
    DOI: 10.1007/s10959-011-0395-y
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    References listed on IDEAS

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    1. Rozkosz, Andrzej, 2004. "On existence of solutions of BSDEs with continuous coefficient," Statistics & Probability Letters, Elsevier, vol. 67(3), pages 249-256, April.
    2. François Coquet & Jean Mémin & Leszek Słomiński, 2003. "On Non-Continuous Dirichlet Processes," Journal of Theoretical Probability, Springer, vol. 16(1), pages 197-216, January.
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