# American Institute of Mathematical Sciences

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

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