Backward stochastic differential equations with locally Lipschitz coefficient

We deal with multidimensional backward stochastic differential equations (BSDE) with locally Lipschitz (in both variables y, z) and sublinear growth coefficient and, an only square integrable terminale data. Let B (O, N) denote the ball of R(d) x R(d x r) and L(N) the Lipschitz constant on B (O, N) of the coefficient. We prove that if L(N) similar to root logN, then the corresponding BSDE has a unique solution. This is the first work which deals with multidimensional BSDE with a local assumption on the coefficient. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.