Comparison theorems for the multidimensional BDSDEs and applications. (English) Zbl 1244.60064

Zhu, Bo; Han, Baoyan

J. Appl. Math. 2012, Article ID 304781, 14 p. (2012).

Summary: 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.

MSC:

60H15

Stochastic partial differential equations (aspects of stochastic analysis)

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