Related papers: Backward stochastic differential equations with ti…
In this paper we discuss backward stochastic differential equations with Markov chain noise, having continuous drivers. We obtain the existence of a solution which is possibly not unique. Moreover, we show there is a minimal solution for…
An existence and uniqueness theorem for a class of stochastic delay differential equations is presented, and the convergence of Euler approximations for these equations is proved under general conditions. Moreover, the rate of almost sure…
In this paper, we study the doubly conditional reflected backward stochastic differential equations (BSDEs), where constraints are made on the conditional expectation of the first component of the solution with respect to a general…
This paper studies the link between the number of critical eigenvalues and the number of delays in certain classes of delay-differential equations. There are two main results. The first states that for k purely imaginary numbers which are…
We provide new results on the existence of extremal solutions for discontinuous differential equations with a deviated argument which can be either delayed or advanced. The boundary condition is allowed to be discontinuous and to depend…
We survey and refine recent results on weak and strong well-posedness of stochastic differential equations with singular drift satisfying some minimal assumptions.
This note aims to give an explicit solution for backward stochastic Volterra integral equations with linear time delayed generators. The process $Y$ is expressed by an integral whose kernel is explicitly given. The processes $Z$ is…
We consider backward stochastic differential equations (BSDEs) related to finite state, continuous time Markov chains. We show that appropriate solutions exist for arbitrary terminal conditions, and are unique up to sets of measure zero. We…
In this paper, we deal with a class of one-dimensional reflected backward doubly stochastic differential equations with one continuous lower barrier. We derive the existence and uniqueness of solutions for these equations with Lipschitz…
The goal of this paper is to solve backward doubly stochastic differential equation (BDSDE, in short) under weak assumptions on the data. The first part is devoted to the development of some new technical aspects of stochastic calculus…
We prove existence and uniqueness of solutions of reflected backward stochastic differential equations in time-dependent adapted and c\`adl\`ag convex regions $\mathcal{D}=\{D_t;t\in[0,T]\}$. We also show that the solution may be…
In this paper, a class of stable explicit $\theta$-schemes are proposed for solving anticipated backward stochastic differential equations (anticipated BSDEs) which generator not only contains the present values of the solutions but also…
We prove existence and uniqueness of L^p solutions of reflected backward stochastic differential equations with p-integrable data and generators satisfying the monotonicity condition. We also show that the solution may be approximated by…
We consider delay differential equations with a polynomially distributed delay. We derive an equivalent system of delay differential equations, which includes just two discrete delays. The stability of the equivalent system and its…
This paper is devoted to the existence, uniqueness and comparison theorem on unbounded solutions of one-dimensional backward stochastic differential equations (BSDEs) with sub-quadratic generators, where the terminal time is allowed to be…
We propose to study a new type of Backward stochastic differential equations driven by a family of It\^o's processes. We prove existence and uniqueness of the solution, and investigate stability and comparison theorem.
In this paper, we consider reflected anticipated backward stochastic differential equations (RABSDEs, for short) with an additional resistance in the generators. Firstly, we study the existence and uniqueness results. In Luo (2020), the…
In this manuscript, we investigate a fractional stochastic neutral differential equation with time delay, which includes both deterministic and stochastic components. Our primary objective is to rigorously prove the existence of a unique…
In the present article, solvability in Sobolev spaces is investigated for a class of degenerate stochastic integro-differential equations of parabolic type. Existence and uniqueness is obtained, and estimates are given for the solution.
The solutions of stochastic differential equations without an external drift are stochastically invariant under time reversal. This singles out the "anti-Ito" integral.