Related papers: Reflected Solutions of Backward Doubly Stochastic …
In this paper we study the homeomorphic properties of the solutions to one dimensional backward doubly stochastic differential equations under suitable assumptions, where the terminal values depend on a real parameter. Then, we apply them…
In this paper, we first prove existence and uniqueness of the solution of a backward doubly stochastic differential equation (BDSDE) and of the related stochastic partial differential equation (SPDE) under monotonicity assumption on the…
The paper studies a multi-dimensional mean-field reflected backward stochastic differential equation (MF-RBSDE) with a reflection constraint depending on both the value process $Y$ and its distribution $[Y]$. We establish the existence,…
In this paper, the stochastic verification theorems for stochastic control problems of reflected forward-backward stochastic differential equations are studied. We carry out the work within the frameworks of classical and viscosity…
We define a class of reflected backward stochastic differential equation (RBSDE) driven by a marked point process (MPP) and a Brownian motion, where the solution is constrained to stay above a given c\`adl\`ag process. The MPP is only…
In this paper, we study a multidimensional backward stochastic differential equation (BSDE) with an additional rough drift (rough BSDE), and give the existence and uniqueness of the adapted solution, either when the terminal value and the…
In this paper, we study a class of reflected backward stochastic differential equations (BSDEs) of mean-field type, where the mean-field interaction in terms of the distribution of the $Y$-component of the solution enters in both the driver…
We study the existence of a solution for a one-dimensional generalized backward stochastic differential equation with two reflecting barriers (GRBSDE for short) under assumptions on the input data which are weaker than that on the current…
In this paper, by introducing a new notion of envelope of the stochastic process, we construct a family of random differential equations whose solutions can be viewed as solutions of a family of ordinary differential equations and prove…
This article introduces and solves a general class of fully coupled forward-backward stochastic dynamics by investigating the associated system of functional differential equations. As a consequence, we are able to solve many different…
We prove the existence of the unique solution of a general Backward Stochastic Differential Equation with quadratic growth driven by martingales. Some kind of comparison theorem is also proved.
We study the problem of existence of solutions for generalized backward stochastic differential equation with two reflecting barriers (GRBSDE for short) under weaker assumptions on the data. Roughly speaking we show the existence of a…
In this paper, we study continuous properties of adapted solutions for backward stochastic differential equations with constraints (CBSDEs in short). Comparing with many existing literatures about this topic, our case is very general in the…
This paper deals with generalized backward doubly stochastic differential equations driven by a L\'evy process (GBDSDEL, in short). Under left or right continuous and linear growth conditions, we prove the existence of minimal (resp.…
In this paper we aim to find the stationary stochastic viscosity solutions of a parabolic type SPDEs through the infinite horizon backward doubly stochastic differential equations (BDSDEs). For this, we study the existence, uniqueness and…
We introduce a discrete time reflected scheme to solve doubly reflected Backward Stochastic Differential Equations with jumps (in short DRBSDEs), driven by a Brownian motion and an independent compensated Poisson process. As in…
In this paper we obtain a Wong-Zakai approximation to solutions of backward doubly stochastic differential equations.
This paper is intended to give a representation for stochastic viscosity solution of semi-linear reflected stochastic partial differential equations with nonlinear Neumann boundary condition. We use its connection with reflected generalized…
We study a discrete time approximation scheme for the solution of a doubly reflected Backward Stochastic Differential Equation (DBBSDE in short) with jumps, driven by a Brownian motion and an independent compensated Poisson process.…
In this paper, we investigate mean-field backward stochastic differential equation (MFBSDE) with double mean reflections and nonlinear resistance. Specifically, the constraints are formulated in terms of the expectation of the solution, and…