arXiv:0808.0801v1 [math.PR] 6 Aug 2008 Backward stochastic variational inequalities under weak assumptions on the data Lucian Maticiuc a,∗ , Aurel R˘ a¸scanu b,c,∗ , Adrian Z˘ alinescu c,∗ a Department of Mathematics, “Gh. Asachi” Technical University of Ia¸si, Bd. Carol I, no. 11, 700506, Romania, b Faculty of Mathematics, “Al.I. Cuza” University of Ia¸si, Bd. Carol I, no. 9, 700506, Romania, c “O. Mayer”Mathematics Institute of the Romanian Academy, Ia¸si, Bd. Carol I, no. 8, 700506, Romania. October 24, 2018 Abstract The aim of this paper is to study the existence and uniqueness of the solution of the backward stochastic differential equations involving the subdifferential operator ∂ϕ (also called backward stochastic variational inequalities):  −dY t + ∂ϕ (Y t ) dt ∋ F (t, Y t ,Z t ) dt − Z t dB t , 0 ≤ t<T Y T = η. Our results generalize those of E. Pardoux and A. R˘ a¸scanu (Stochastic Processes and their Applications 76, 1998) to the case in which the function F satisfies a local boundeness condition (instead of sublinear growth condition with respect to y). AMS Classification subjects: 60H10, 93E03, 47J20, 49J40. Keywords: Backward stochastic differential equations; Subdifferential operators; Stochastic variational inequalities. 1 Introduction We consider the following backward stochastic variational inequality (BSVI)  −dY t + ∂ϕ (Y t ) dt ∋ F (t,Y t ,Z t ) dt − Z t dB t , 0 ≤ t<T Y T = η. (1) * The work was supported by Grants ID 395/2007, CEEX 05-D11-36/2005, CNCSIS 1373/2007 E-mail addresses: lucianmaticiuc@yahoo.com (Lucian Maticiuc), aurel.rascanu@uaic.ro (Aurel R˘ a¸scanu), adrian.zalinescu@gmail.com (Adrian Z˘alinescu). 1