Reflected Solutions of Backward Doubly Stochastic Differential Equations

Weiqiang Yang, Yufeng Shi, Yangling Gu

Published 2008-06-05, updated 2009-06-08Version 2

We study reflected solutions of one-dimensional backward doubly stochastic differential equations (BDSDEs in short). The "reflected" keeps the solution above a given stochastic process. We get the uniqueness and existence by penalization. For the existence of backward stochastic integral, our proof is different from [KKPPQ] slightly. We also obtain a comparison theorem for reflected BDSDEs.