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Comparison theorems of backward doubly stochastic differential equations and applications. (English) Zbl 1067.60046
The authors obtain a comparison theorem for a class of backward doubly stochastic differential equations (BDSDEs for short). As one of its applications, the existence of solutions for BDSDEs with continuous coefficients is derived. For one-dimensional BDSDEs, the authors weaken the usual Lipschitz assumptions to linear growth conditions by virtue of the comparison theorem. The existence of the minimal solution of BDSDEs is shown.

MSC:
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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