Some uniqueness results for one-dimensional BSDEs with uniformly continuous coefficients

In this note we discuss one-dimensional backward stochastic differential equations (BSDEs) with coefficient g which is uniformly continuous in (y, z). As we know, the solution to this kind of BSDE may be non-unique. We prove that, the set of real numbers c such that the solution of perturbed BSDE with coefficient g + c is non-unique. is at most countable, and we give some necessary and sufficient conditions for the uniqueness for solution to this kind of BSDEs. More importantly, we prove that if g is independent of y, the solution of corresponding BSDE is unique. (C) 2008 Elsevier B.V. All rights reserved.