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Variational approach for the adapted solution of the general backward stochastic differential equations under the Bihari condition

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  • Qin, Yan
  • Xia, Ning-Mao

Abstract

In this paper, we study the existence and uniqueness of the adapted solution of a backward stochastic differential equation with a general diffusion coefficient. By using the idea of Brownian bridge, and changing the control term from the diffusion coefficient to the drift coefficient, we prove the existence of the solution under the Bihari condition, which extends the E-well posed condition (Peng, 1994). The uniqueness properties of the solution are also discussed in this paper.

Suggested Citation

  • Qin, Yan & Xia, Ning-Mao, 2013. "Variational approach for the adapted solution of the general backward stochastic differential equations under the Bihari condition," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1271-1281.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:4:p:1271-1281
    DOI: 10.1016/j.spl.2013.01.025
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    References listed on IDEAS

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    1. Mao, Xuerong, 1995. "Adapted solutions of backward stochastic differential equations with non-Lipschitz coefficients," Stochastic Processes and their Applications, Elsevier, vol. 58(2), pages 281-292, August.
    2. 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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