Related papers: Conditional Expectation Backward Stochastic Differ…
We study a system of Forward-Backward Stochastic Differential Equations (FBSDEs) with time-delayed generators. The forward process includes a reflection component expressed via a Stieltjes integral, while the backward process takes the form…
This paper is dedicated to the analysis of backward stochastic differential equations (BSDEs) with jumps, subject to an additional global constraint involving all the components of the solution. We study the existence and uniqueness of a…
This paper focuses on inverse problems to identify parameters by incorporating information from measurements. These generally ill-posed problems are formulated here in a probabilistic setting based on Bayes's theorem because it leads to a…
This paper is concerned with the quasi-linear reflected backward stochastic partial differential equation (RBSPDE for short). Basing on the theory of backward stochastic partial differential equation and the parabolic capacity and…
We consider systems of backward stochastic differential equations with c\`adl\`ag upper barrier $U$ and oblique reflection from below driven by an increasing continuous function $H$. Our equations are defined on general probability spaces…
This paper investigates optimal control problems for delayed systems governed by Infinitely Anticipated Backward Stochastic Differential Equations (IABSDEs). Unlike existing frameworks limited to bounded delays, we introduce a generalized…
We give a theory of sublinear expectations and martingales in discrete time. Without assuming the existence of a dominating probability measure, we derive the extensions of classical results on uniform integrability, optional stopping of…
In this note, we study one-dimensional reflected backward doubly stochastic differential equations (RBDSDEs) with one continuous barrier and discontinuous generator (left-or right-continuous). By a comparison theorem establish here for…
We introduce a new formulation of reflected BSDEs and doubly reflected BSDEs associated with irregular obstacles. In the first part of the paper, we consider an extension of the classical optimal stopping problem over a larger set of…
In this paper, we consider a stochastic decision problem for a system governed by a stochastic differential equation, in which an optimal decision is made in such a way to minimize a vector-valued accumulated cost over a finite-time horizon…
This paper is devoted to study different type of BSDE with delayed generator. We first establish an existence and uniqueness result under delayed Lipschitz condition for non homogenous backward stochastic differential equation with delayed…
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…
In this paper, we derive sufficient conditions for each component of the solution to a general backward stochastic differential equation to have a density for which upper and lower Gaussian estimates can be obtained.
We formulate a new class of stochastic partial differential equations (SPDEs), named high-order vector backward SPDEs (B-SPDEs) with jumps, which allow the high-order integral-partial differential operators into both drift and diffusion…
We consider reflected backward stochastic different equations with optional barrier and so-called regulated trajectories, i.e trajectories with left and right finite limits. We prove existence and uniqueness results. We also show that the…
This paper investigate a class of multi-dimensional backward stochastic differential equations (BSDEs) with singualr generators exhibiting diagonally quadratic growth and unbounded terminal conditions, thereby extending results in the…
In this paper, we introduce a new kind of reflected backward stochastic differential equations (RBSDEs) driven by a martingale, in a Markov chain model, but not driven by Brownian motion, and give existence and uniqueness results for the…
Delayed processes are ubiquitous in biological systems and are often characterized by delay differential equations (DDEs) and their extension to include stochastic effects. DDEs do not explicitly incorporate intermediate states associated…
In this paper we introduce a model, the stochastic fractional delay differential equation (SFDDE), which is based on the linear stochastic delay differential equation and produces stationary processes with hyperbolically decaying…
In this paper, we focus on mean-field anticipated backward stochastic differential equations (MF-BSDEs, for short) driven by fractional Brownian motion with Hurst parameter H>1/2. First, the existence and uniqueness of this new type of…