L p solutions of Backward Stochastic Dierential Equations

In this paper we are interested in solving backward stochastic dierential equations (BSDEs for short) under weak assumptions on the data. The first part of the paper is devoted to the development of some new technical aspects of stochastic calculus related to BSDEs. Then we derive apriori estimates and prove existence and uniqueness of solutions in L p p > 1, extending the results of [3] to the case where the monotonicity conditions of [6] are satisfied. We consider both a fixed and a random time interval. In the last section, we obtain, under an additional assumption, an existence and uniqueness result for BSDEs on a fixed time interval, when the data are only in L 1 .