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Weak solutions of backward stochastic differential equations with continuous generator

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  • Bouchemella, Nadira
  • Raynaud de Fitte, Paul

Abstract

We prove the existence of a weak solution to a backward stochastic differential equation (BSDE) Yt=ξ+∫tTf(s,Xs,Ys,Zs)ds−∫tTZsdWs in a finite-dimensional space, where f(t,x,y,z) is affine with respect to z, and satisfies a sublinear growth condition and a continuity condition. This solution takes the form of a triplet (Y,Z,L) of processes defined on an extended probability space and satisfying Yt=ξ+∫tTf(s,Xs,Ys,Zs)ds−∫tTZsdWs−(LT−Lt) where L is a martingale with possible jumps which is orthogonal to W. The solution is constructed on an extended probability space, using Young measures on the space of trajectories. One component of this space is the Skorokhod space D endowed with the topology S of Jakubowski.

Suggested Citation

  • Bouchemella, Nadira & Raynaud de Fitte, Paul, 2014. "Weak solutions of backward stochastic differential equations with continuous generator," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 927-960.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:1:p:927-960
    DOI: 10.1016/j.spa.2013.09.011
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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.
    2. Delarue, F. & Guatteri, G., 2006. "Weak existence and uniqueness for forward-backward SDEs," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1712-1742, December.
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