Related papers: A Framework of BSDEs with Stochastic Lipschtz Coef…
A new explicit stochastic scheme of order 1 is proposed for solving commutative stochastic differential equations (SDEs) with non-globally Lipschitz continuous coefficients. The proposed method is a semi-tamed version of Milstein scheme to…
This paper establishes an existence and uniqueness result for the adapted solution of a general time interval multidimensional backward stochastic differential equation (BSDE), where the generator $g$ satisfies a weak…
In this paper, the stability behaviors of stochastic differential equations (SDEs) driven by time-changed Brownian motions are discussed. Based on the generalized Lyapunov method and stochastic analysis, necessary conditions are provided…
This paper is devoted to solving a multidimensional backward stochastic differential equation with a general time interval, where the generator is uniformly continuous in $(y,z)$ non-uniformly with respect to $t$. By establishing some…
We prove well-posedness results for backward stochastic differential equations (BSDEs) and reflected BSDEs with an optional obstacle process in the case of appropriately weighted $\mathbb{L}^2$-data when the generator is integrated with…
In this paper, we study the global solvability of multidimensional forward-backward stochastic differential equations (FBSDEs) with diagonally Lipschitz, quadratic or super-quadratic generators. Under a certain "monotonicity" condition, we…
This paper investigates a non-autonomous slow-fast system, which is generalized by stochastic differential equations (SDEs) with locally Lipschitz coefficients, subjected to standard Brownian motion (Bm) and fractional Brownian motion (fBm)…
We provide existence results and comparison principles for solutions of backward stochastic difference equations (BS$\Delta$Es) and then prove convergence of these to solutions of backward stochastic differential equations (BSDEs) when the…
We study generalized backward stochastic differential equations (BSDEs) up to a random time horizon $\vartheta$, which is not a stopping time, under minimal assumptions regarding the properties of $\vartheta$. In contrast to existing works…
This study focuses on a multidimensional backward stochastic differential equation (BSDE) with a general random terminal time $\tau$ taking values in $[0,+\infty]$. The generator $g$ satisfies a stochastic monotonicity condition in the…
We consider a one-dimensional stochastic differential equations (SDE) with irregular coefficients. The purpose of this paper is to estimate the $L^p(\Omega)$-difference of SDEs using the norm of the difference of coefficients, where the…
We study linear backward stochastic partial differential equations of parabolic type with special boundary condition that connect the terminal value of the solution with a functional over the entire past solution. Uniqueness, solvability…
In this paper, we are interested in solving general time interval multidimensional backward stochastic differential equations in $L^p$ $(p\geq 1)$. We first study the existence and uniqueness for $L^p$ $(p>1)$ solutions by the method of…
In this paper, we introduce a new type of backward stochastic differential equations (BSDEs) with infinite anticipation, where the generator depends on the entire future values of the solution in infinite horizon. We show that the new BSDEs…
This paper is concerned with existence and uniqueness of M-solutions of backward stochastic Volterra integral equations (BSVIEs for short), which Lipschitz coefficients are allowed to be random, which generalize the results in [15]. Then a…
In this paper, we prove new convergence results improving the ones by Chassagneux, Elie and Kharroubi [Ann. Appl. Probab. 22 (2012) 971--1007] for the discrete-time approximation of multidimensional obliquely reflected BSDEs. These BSDEs,…
This paper aims at solving one-dimensional backward stochastic differential equations (BSDEs) under weaker assumptions. We establish general existence, uniqueness, and comparison results for bounded solutions, $L^p (p>1)$ solutions and…
We are concerned with the discretization of a solution of a Forward-Backward stochastic differential equation (FBSDE) with a jump process depending on the Brownian motion. In this paper, we study the cases of Lipschitz generators and the…
In this article, we are interested in solving numerically backward doubly stochastic differential equations (BDSDEs) with random terminal time tau. The main motivations are giving a probabilistic representation of the Sobolev's solution of…
In this paper we discuss new types of differential equations which we call anticipated backward stochastic differential equations (anticipated BSDEs). In these equations the generator includes not only the values of solutions of the present…