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On existence of solutions of BSDEs with continuous coefficient

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  • Rozkosz, Andrzej

Abstract

We consider one-dimensional backward stochastic differential equation driven by diffusion corresponding to a symmetric uniformly elliptic divergence form operator. We show that in the case where the coefficient of the equation is continuous and satisfies the linear growth condition there is a solution of the equation which has a representation in terms of a Sobolev solution of the corresponding semilinear partial differential equation.

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  • Rozkosz, Andrzej, 2004. "On existence of solutions of BSDEs with continuous coefficient," Statistics & Probability Letters, Elsevier, vol. 67(3), pages 249-256, April.
    • Handle: RePEc:eee:stapro:v:67:y:2004:i:3:p:249-256
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    References listed on IDEAS

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    1. Lepeltier, J. P. & San Martin, J., 1997. "Backward stochastic differential equations with continuous coefficient," Statistics & Probability Letters, Elsevier, vol. 32(4), pages 425-430, April.
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    Cited by:

    1. 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.

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