A Kneser-type theorem for backward doubly stochastic differential equations

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November 2010, 14(4): 1565-1579. doi: 10.3934/dcdsb.2010.14.1565

A Kneser-type theorem for backward doubly stochastic differential equations

1.	Institute for Financial Studies and School of Mathematics, Shandong University, Jinan, Shandong 250100, China
2.	School of Statistics and Mathematics, Shandong University of Finance, Jinan, Shandong 250014, China

Received July 2009 Revised February 2010 Published August 2010

Abstract
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A class of backward doubly stochastic differential equations (BDSDEs in short) with continuous coefficients is studied. We give the comparison theorems, the existence of the maximal solution and the structure of solutions for BDSDEs with continuous coefficients. A Kneser-type theorem for BDSDEs is obtained. We show that there is either unique or uncountable solutions for this kind of BDSDEs.

Keywords: maximal solution, Backward doubly stochastic differential equations, Kneser-type theorem., comparison theorem.

Mathematics Subject Classification: 60H1.

Citation: Yufeng Shi, Qingfeng Zhu. A Kneser-type theorem for backward doubly stochastic differential equations. Discrete & Continuous Dynamical Systems - B, 2010, 14 (4) : 1565-1579. doi: 10.3934/dcdsb.2010.14.1565

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