Reflected Solutions of Backward Doubly Stochastic Differential Equations

Details Reflected Solutions of Backward Doubly Stochastic Differential Equations Reflected Solutions of Backward Doubly Stochastic Differential Equations

2008-06-05

arxiv.org/abs/0806.0917v2

Mathematics

Probability

18 pages

Scientific paper

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.

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