  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).
