Related papers: Representation theorems for backward doubly stocha…
We provide a stochastic representation for a general class of viscous Hamilton-Jacobi (HJ) equations, which has convexity and superlinear nonlinearity in its gradient term, via a type of backward stochastic differential equation (BSDE) with…
We provide a representation formula for viscosity solutions to a class of nonlinear second order parabolic PDEs given as a sup--envelope function. This is done through a dynamic programming principle derived from Denis, Hu, Peng (2010). The…
Mean-field backward doubly stochastic differential equations (MF-BDSDEs, for short) are introduced and studied. The existence and uniqueness of solutions for MF-BDSDEs is established. One probabilistic interpretation for the solutions to a…
In this paper we present two numerical schemes of approximating solutions of backward doubly stochastic differential equations (BDSDEs for short). We give a method to discretize a BDSDE. And we also give the proof of the convergence of…
By using a simple observation that the density processes appearing in Ito's martingale representation theorem are invariant under the change of measures, we establish a non-linear version of the Cameron-Martin formula for solutions of a…
The connection between forward backward doubly stochastic differential equations and the optimal filtering problem is established without using the Zakai's equation. The solutions of forward backward doubly stochastic differential equations…
We prove an $L^2$-regularity result for the solutions of Forward Backward Doubly Stochastic Differentiel Equations (FBDSDEs in short) under globally Lipschitz continuous assumptions on the coefficients. Therefore, we extend the well known…
We investigate two-barriers-reflected backward stochastic differential equations with data from rank-based stochastic differential equation. More specifically, we focus on the solution of backward stochastic differential equations…
In this work, we prove existence and uniqueness of a bounded viscosity solution for the Cauchy problem of degenerate parabolic equations with variable exponent coefficients. We construct the solution directly using the stochastic…
Backward stochastic differential equations extend the martingale representation theorem to the nonlinear setting. This can be seen as path-dependent counterpart of the extension from the heat equation to fully nonlinear parabolic 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…
In this paper, our goal is solving backward doubly stochastic differential equation (BDSDE for short) under weak assumptions on the data. The first part of the paper is devoted to the development of some new technical aspects of stochastic…
We introduce a class of second order backward stochastic differential equations and show relations to fully non-linear parabolic PDEs. In particular, we provide a stochastic representation result for solutions of such PDEs and discuss Monte…
This paper, is an attempt to extend the notion of stochastic viscosity solution to reflected semi-linear stochastic partial differential equations (RSPDEs, in short) with non-Lipschitz condition on the coefficients. Our method is fully…
In this paper, we consider the Cauchy problem of semi-linear degenerate backward stochastic partial differential equations (BSPDEs in short) under general settings without technical assumptions on the coefficients. For the solution of…
This paper introduces a class of backward stochastic differential equations (BSDEs), whose coefficients not only depend on the value of its solutions of the present but also the past and the future. For a sufficiently small time delay or a…
In this paper, we introduce a specific kind of doubly reflected Backward Stochastic Differential Equations (in short DRBSDEs), defined on probability spaces equipped with general filtration that is essentially non quasi-left continuous,…
In this paper, a class of non-Markovian forward-backward doubly stochastic systems is studied. By using the technique of functional It\^o (or path-dependent) calculus, the relationship between the systems and related path-dependent…
In this work, we study the numerical approximation of a class of singular fully coupled forward backward stochastic differential equations. These equations have a degenerate forward component and non-smooth terminal condition. They are…
In this paper, we study reflected backward stochastic differential equation (reflected BSDE in abbreviation) with rank-based data in a Markovian framework; that is, the solution to the reflected BSDE is above a prescribed boundary process…