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Comparison Theorems for the Multidimensional BDSDEs and Applications

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Listed:
  • Bo Zhu
  • Baoyan Han

Abstract

A class of backward doubly stochastic differential equations (BDSDEs) are studied. We obtain a comparison theorem of these multidimensional BDSDEs. As its applications, we derive the existence of solutions for this multidimensional BDSDEs with continuous coefficients. We can also prove that this solution is the minimal solution of the BDSDE.

Suggested Citation

  • Bo Zhu & Baoyan Han, 2012. "Comparison Theorems for the Multidimensional BDSDEs and Applications," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:304781
    DOI: 10.1155/2012/304781
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    References listed on IDEAS

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    1. V. Bally & A. Matoussi, 2001. "Weak Solutions for SPDEs and Backward Doubly Stochastic Differential Equations," Journal of Theoretical Probability, Springer, vol. 14(1), pages 125-164, January.
    2. Geiß, Christel & Manthey, Ralf, 1994. "Comparison theorems for stochastic differential equations in finite and infinite dimensions," Stochastic Processes and their Applications, Elsevier, vol. 53(1), pages 23-35, September.
    3. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
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    Cited by:

    1. Bo Zhu & Baoyan Han, 2012. "Stochastic PDEs and Infinite Horizon Backward Doubly Stochastic Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).

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