Related papers: Asymptotic behavior for delayed backward stochasti…
We establish sufficient conditions for the existence and uniqueness of mean-field backward stochastic differential equations with time delayed generator in the sense that at t, the generator may depend on previous values up to a delay…
In this paper, we study the asymptotic behavior of solutions to a scalar fractional delay differential equations around the equilibrium points. More precise, we provide conditions on the coefficients under which a linear fractional delay…
In this paper, we consider asymptotic behaviors of multiscale multivalued stochastic systems with small noises. First of all, for general, fully coupled systems for multivalued stochastic differential equations of slow and fast motions with…
The main contributions of this paper are three fold. First, our primary concern is to investigate a class of stochastic recursive delayed control problems which arise naturally with sound backgrounds but have not been well-studied yet. For…
In this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-called characteristic function of our system is completely…
Some problems in the theory and applications of stochastic processes can be reduced to solving integral equations. While explicit solutions for these equations are often elusive, valuable insights can be gained through their asymptotic…
In this paper, we study the solvability of anticipated backward stochastic differential equations (BSDEs, for short) with quadratic growth for one-dimensional case and multi-dimensional case. In these BSDEs, the generator, which is of…
The present paper is devoted to the well-posedness of a type of multi-dimensional backward stochastic differential equations (BSDEs) with a diagonally quadratic generator. We give a new priori estimate, and prove that the BSDE admits a…
The aim of this article is to study the asymptotic behaviour for large times of solutions to a certain class of stochastic partial differential equations of parabolic type. In particular, we will prove the backward uniqueness result and 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…
The main purpose of this paper is to provide a summary of the fundamental methods for analyzing delay differential equations arising in biology and medicine. These methods are employed to illustrate the effects of time delay on the behavior…
In this paper we classify the pathwise asymptotic behaviour of the discretisation of a general autonomous scalar differential equation which has a unique and globally stable equilibrium. The underlying continuous equation is subjected to a…
A splitting scheme for backward doubly stochastic differential equations is proposed. The main idea is to decompose a backward doubly stochastic differential equation into a backward stochastic differential equation and a stochastic…
In this paper, we establish a large deviation principle for the conservative stochastic partial differential equations, whose solutions are related to stochastic differential equations with interaction. The weak convergence method and the…
In backward error analysis, an approximate solution to an equation is compared to the exact solution to a nearby modified equation. In numerical ordinary differential equations, the two agree up to any power of the step size. If the…
We present a general method for studying long time asymptotics of nonlinear parabolic partial differential equations. The method does not rely on a priori estimates such as the maximum principle. It applies to systems of coupled equations,…
We study the large time behavior of solutions to fully nonlinear parabolic equations of Hamilton-Jacobi-Bellman type arising typically in stochastic control theory with control both on drift and diffusion coefficients. We prove that, as…
Retarded stochastic differential equations (SDEs) constitute a large collection of systems arising in various real-life applications. Most of the existing results make crucial use of dissipative conditions. Dealing with "pure delay" systems…
The large deviations principles are established for a class of multidimensional degenerate stochastic differential equations with reflecting boundary conditions. The results include two cases where the initial conditions are adapted and…
This article is devoted to study the class of backward stochastic differential equation with delayed generator. We suppose the terminal value and the generator to be $L^{p}$-integrable with $p>1$. We derive a new type of estimation related…