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

Andrzej Rozkosz ()
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Andrzej Rozkosz: Nicolaus Copernicus University

Journal of Theoretical Probability, 2013, vol. 26, issue 4, 1061-1083

Abstract: 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.

Keywords: Backward stochastic differential equation; Viscous conservation law; Weak solution; Feynman–Kac formula; 60H99; 35K58 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10959-011-0395-y

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