In this paper, on the basis of some recent works Fan, Jiang and Jia, we establish a representation theorem in space processes for generators BSDEs with monotonic polynomial-growth generators, which generalizes corresponding results Fan (2006, 2007), Hu (2008).

We prove a uniqueness result of the unbounded solution for quadratic backward stochastic differential equation whose terminal condition is and generator g may be non-Lipschitz continuous in state variable y non-convex (non-concave) z, instead satisfies strictly an additional assumption. The key observation that if quadratic, then variation first component admits exponential moment. Typically, Lipschitz perturbation some convex (concave) function assumption mentioned above. This generalizes...

This paper puts forward the basic form of stochastic Gronwall's inequality and uses, respectively, iterative method, integral method martingale representation to prove it. Then it presents an application a comparison theorem Lp solutions for one-dimensional backward differential equations under Lipschitz condition.

This paper deals with bounded solutions for general time interval one-dimensional backward stochastic differential equations (BSDEs short) quadratic growth coefficients and conditions. Several results of existence, uniqueness, stability comparison the are put forward established, which improve considerably some existing works, even though case finite interval. Some new ideas also developed to establish these results.

In [8], the existence of solution is proved for a scalar linearly growingbackward stochastic differential equation (BSDE) when terminal value is$L\exp (\mu \sqrt{2\log (1+L)} )$-integrable positive parameter $\mu >\mu _{0}$ with critical _{0}$, and counterexample provided to show that preceding integrability <\mu not sufficient guarantee solution. Afterwards, uniqueness result (with _{0}$) also given in [3] BSDE under uniformly Lipschitz condition generator. this note, we prove these two...

The main purpose of this paper is to prove an existence and uniqueness result for solutions a multidimensional backward stochastic differential equation (BSDE) with general time interval (including the deterministic cases), where generator g BSDE weakly monotonic growth in y, Lipschitz continuous z, both non-uniformly respect t. And, corresponding comparison theorem one-dimensional BSDEs provided. As applications, we establish nonlinear Doob-Meyer’s decomposition g-supermartingales under...