Related papers: Convergence of the Euler-Maruyama method for multi…
The Euler scheme is one of the standard schemes to obtain numerical approximations of stochastic differential equations (SDEs). Its convergence properties are well-known in the case of globally Lipschitz continuous coefficients. However, in…
In this paper the numerical approximation of stochastic differential equations satisfying a global monotonicity condition is studied. The strong rate of convergence with respect to the mean square norm is determined to be $\frac{1}{2}$ for…
We study in this article the strong rate of convergence of the Euler-Maruyama scheme and associated with the jump-type equation introduced in Li and Mytnik. We obtain the strong rate of convergence under similar assumptions for strong…
The aim of this paper is to study weak and strong convergence of the Euler--Maruyama scheme for a solution of one-dimensional degenerate stochastic differential equation $\mathrm{d} X_t=\sigma(X_t) \mathrm{d} W_t$ with non-sticky condition.…
The strong rate of convergence of the Euler-Maruyama scheme for nondegenerate SDEs with irregular drift coefficients is considered. In the case of $\alpha$-H\"older drift in the recent literature the rate $\alpha/2$ was proved in many…
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…
In this paper, we investigate the weak convergence rate of Euler-Maruyama's approximation for stochastic differential equations with irregular drifts. Explicit weak convergence rates are presented if drifts satisfy an integrability…
In this paper, we examine the performance of randomised Euler-Maruyama (EM) method for additive time-inhomogeneous SDEs with an irregular drift. In particular, the drift is assumed to be $\alpha$-H\"older continuous in time and bounded…
For stochastic differential equations (SDEs) with Markovian switching, whose drift and diffusion coefficients are allowed to contain superlinear terms, the backward Euler-Maruyama (BEM) method is proposed to approximate the invariant…
A new class of explicit Euler schemes, which approximate stochastic differential equations (SDEs) with superlinearly growing drift and diffusion coefficients, is proposed in this article. It is shown, under very mild conditions, that these…
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.…
The strong convergence of the semi-implicit Euler-Maruyama (EM) method for stochastic differential equations with non-linear coefficients driven by a class of L\'evy processes is investigated. The dependence of the convergence order of the…
In this paper, we extend the logarithmic Euler-Maruyama scheme for stochastic delay differential equation in one dimension to the part where we propose a scheme for a system of stochastic delay differential equations. We then show that the…
Euler-Maruyama method is studied to approximate stochastic differential equations driven by the symmetric $\alpha$-stable additive noise with the $\beta$ H\"older continuous drift coefficient. When $\alpha \in (1,2)$ and $\beta \in…
The backward Euler-Maruyama (BEM) method is employed to approximate the invariant measure of stochastic differential equations, where both the drift and the diffusion coefficient are allowed to grow super-linearly. The existence and…
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 introduce the Multilevel Euler-Maruyama (ML-EM) method compute solutions of SDEs and ODEs using a range of approximators $f^1,\dots,f^k$ to the drift $f$ with increasing accuracy and computational cost, only requiring a few evaluations…
The approximation of invariant measures for nonlinear ergodic stochastic differential equations (SDEs) is a central problem in scientific computing, with important applications in stochastic sampling, physics, and ecology. We first propose…
This paper investigates longtime behaviors of the $\theta$-Euler-Maruyama method for the stochastic functional differential equation with superlinearly growing coefficients. We focus on the longtime convergence analysis in mean-square sense…
In this paper we extend existing results on the numerical approximation of one-dimensional SDEs with drift in a negative order Besov space and driven by Brownian motion. Using the Yamada-Watanabe approximation technique, we prove rates in…