L^{p}-solutions of backward doubly stochastic differential equations

Details L^{p}-solutions of backward doubly stochastic differential equations L^{p}-solutions of backward doubly stochastic differential equations

2010-11-12

arxiv.org/abs/1011.3030v2

Mathematics

Probability

The version has been greatly improved and is accepted for publication in Stochastic and Dynamics

Scientific paper

The goal of this paper is to solve backward doubly stochastic differential equation (BDSDE, in short) under weak assumptions on the data. The first part is devoted to the development of some new technical aspects of stochastic calculus related to BDSDEs. Then we derive a priori estimates and prove existence and uniqueness of solutions in Lp, p\in (1,2), extending the work of pardoux and Peng (see Probab. Theory Related Fields 98 (1994), no. 2).

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