Related papers: A note on strong convergence of implicit scheme fo…
On the one hand, the explicit Euler scheme fails to converge strongly to the exact solution of a stochastic differential equation (SDE) with a superlinearly growing and globally one-sided Lipschitz continuous drift coefficient. On the other…
This manuscript is dedicated to the numerical approximation of super-linear slow-fast stochastic differential equations (SFSDEs). Borrowing the heterogeneous multiscale idea, we propose an explicit multiscale Euler-Maruyama scheme suitable…
This paper focuses on explicit approximations for nonlinear stochastic delay differential equations (SDDEs). Under the weakly local Lipschitz and some suitable conditions, a generic truncated Euler-Maruyama (TEM) scheme for SDDEs is…
We consider the approximation of stochastic differential equations (SDEs) with non-Lipschitz drift or diffusion coefficients. We present a modified explicit Euler-Maruyama discretisation scheme that allows us to prove strong convergence,…
In this paper we study the existence and uniqueness of the random periodic solution for a stochastic differential equation with a one-sided Lipschitz condition (also known as monotonicity condition) and the convergence of its numerical…
We construct a nonstandard finite difference numerical scheme to approximate stochastic differential equations (SDEs) using the idea of weighed step introduced by R.E. Mickens. We prove the strong convergence of our scheme under locally…
This paper is concerned with strong convergence of a tamed $\theta$-Euler-Maruyama scheme for neutral stochastic differential delay equations with superlinearly growing coefficients. We not only prove the strong convergence of implicit…
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…
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,…
The strong convergence of Euler approximations of stochastic delay differential equations is proved under general conditions. The assumptions on drift and diffusion coefficients have been relaxed to include polynomial growth and only…
Since it is difficult to implement implicit schemes on the infinite-dimensional space, we aim to develop the explicit numerical method for approximating super-linear stochastic functional differential equations (SFDEs). Precisely, borrowing…
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…
Many stochastic differential equations (SDEs) in the literature have a superlinearly growing nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the computationally efficient Euler-Maruyama approximation method…
We study the convergence of a generic tamed Euler-Maruyama (EM) scheme for the kinetic type stochastic differential equations (SDEs) (also known as second order SDEs) with singular coefficients in both weak and strong probabilistic senses.…
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…
We consider the Euler-Maruyama approximation for multi-dimensional stochastic differential equations with irregular coefficients. We provide the rate of strong convergence where the possibly discontinuous drift coefficient satisfies a…
In this paper numerical methods for solving stochastic differential equations with Markovian switching (SDEwMSs) are developed by pathwise approximation. The proposed family of strong predictor-corrector Euler-Maruyama methods is designed…
An Euler-type framework with equidistant step sizes is proposed for a class of time-changed stochastic differential equations.We establish the strong convergence rate of the standard Euler--Maruyama method under the global Lipschitz…
We survey recent developments in the field of complexity of pathwise approximation in $p$-th mean of the solution of a stochastic differential equation at the final time based on finitely many evaluations of the driving Brownian motion.…
The strong convergence of numerical methods for stochastic differential equations (SDEs) for $t\in[0,\infty)$ is proved. The result is applicable to any one-step numerical methods with Markov property that have the finite time strong…