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The paper is focused on the nonlinear stability analysis of stochastic $\theta$-methods. In particular, we consider nonlinear stochastic differential equations such that the mean-square deviation between two solutions exponentially decays,…
Stochastic differential equations (SDEs) on Riemannian manifolds have numerous applications in system identification and control. However, geometry-preserving numerical methods for simulating Riemannian SDEs remain relatively…
The (asymptotic) behaviour of the second moment of solutions to stochastic differential equations is treated in mean-square stability analysis. This property is discussed for approximations of infinite-dimensional stochastic differential…
Polynomial stability of exact solution and modified truncated Euler-Maruyama method for stochastic differential equations with time-dependent delay are investigated in this paper. By using the well known discrete semimartingale convergence…
In this paper we investigate explicit numerical approximations for stochastic differential delay equations (SDDEs) under a local Lipschitz condition by employing the adaptive Euler-Maruyama (EM) method. Working in both finite and infinite…
In this paper, we investigate the convergence of the tamed Euler-Maruyama (EM) scheme for a class of neutral stochastic differential delay equations. The strong convergence results of the tamed EM scheme are presented under global and local…
In this paper, we are concerned with convergence rate of Euler-Maruyama (EM) scheme for stochastic differential delay equations (SDDEs) of neutral type, where the neutral term, the drift term and the diffusion term are allowed to be of…
Exponential stability of the exact solutions as well as $\theta$-EM ($\frac{1}{2}<\theta\le 1$) approximations to neutral stochastic differential delay equations with Markov switching will be investigated in this paper. Sufficient…
Stochastic differential equations with noisy memory are often impossible to solve analytically. Therefore, we derive a numerical Euler-Maruyama scheme for such equations and prove that the mean-square error of this scheme is of order…
This work focuses on the numerical approximations of neutral stochastic delay differential equations with their drift and diffusion coefficients growing super-linearly with respect to both delay variables and state variables. Under…
This paper focuses on the numerical scheme for multiple-delay stochastic differential equations with partially H\"older continuous drifts and locally H\"older continuous diffusion coefficients. To handle with the superlinear terms in…
We prove a general criterion providing sufficient conditions under which a time-discretiziation of a given Stochastic Differential Equation (SDE) is a uniform in time approximation of the SDE. The criterion is also, to a certain extent,…
This paper investigates the approximation of stochastic delay differential equations (SDDEs) via the backward Euler-Maruyama (BEM) method under generalized monotonicity and Khasminskii-type conditions in the infinite horizon. First, by…
We are interested in the strong convergence and almost sure stability of Euler-Maruyama (EM) type approximations to the solutions of stochastic differential equations (SDEs) with non-linear and non-Lipschitzian coefficients. Motivation…
The aim of this paper is to investigate strong convergence of modified truncated Euler-Maruyama method for neutral stochastic differential delay equations introduced in Lan (2018). Strong convergence rates of the given numerical scheme to…
We propose a stochastic model predictive control (SMPC) framework for a broad class of unconstrained controlled stochastic differential equations (SDEs) and establish its mean-square exponential stability in the infinite-horizon limit. At…
In this paper, the stability of $\theta$-methods for delay differential equations is studied based on the test equation $y'(t)=-A y(t) + B y(t-\tau)$, where $\tau$ is a constant delay and $A$ is a positive definite matrix. It is mainly…
In this paper we investigate the mean square asymptotic stability of a perturbed scalar linear stochastic functional differential equation. Specifically, we are able to give necessary and sufficient conditions on the forcing terms for…
The exponential stability, in both mean square and almost sure senses, for energy solutions to a class of nonlinear and non-autonomous stochastic PDEs with finite memory is investigated. Various criteria for stability are obtained. An…
In this paper we investigate the convergence rate of Euler-Maruyama scheme for a class of stochastic differential delay equations, where the corresponding coefficients may be highly nonlinear with respect to the delay variables. In…