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In this paper, a modified Euler-Maruyama (EM) method is constructed for a kind of multi-term Riemann-Liouville stochastic fractional differential equations and the strong convergence order min{1-{\alpha}_m, 0.5} of the proposed method is…

Numerical Analysis · Mathematics 2022-05-10 Jingna Zhang , Jianfei Huang , Yifa Tang , Luis Vázquez

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…

Numerical Analysis · Mathematics 2012-04-10 Xuerong Mao , Lukasz Szpruch

In this work, we present a general technique for establishing the strong convergence of numerical methods for stochastic delay differential equations (SDDEs) in the infinite horizon. This technique can also be extended to analyze certain…

Numerical Analysis · Mathematics 2025-05-21 Yudong Wang , Hongjiong Tian

This paper investigates the approximation of invariant measures for McKean-Vlasov stochastic differential equations (SDEs) using the Euler-Maruyama (EM) scheme under a monotonicity condition. Firstly, the convergence of the numerical…

Probability · Mathematics 2026-04-17 Zhen Wang , Mingyan Wu

Recently, Martin Hutzenthaler pointed out that the explicit Euler method fails to converge strongly to the exact solution of a stochastic differential equation (SDE) with superlinearly growing and globally one sided Lipschitz drift…

Numerical Analysis · Mathematics 2015-02-03 M. H. Song , Y. L. Lu , M. Z. Liu

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…

Probability · Mathematics 2025-01-28 Jianhai Bao , Yue Wu

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…

Probability · Mathematics 2017-07-10 Li Tan , Chenggui Yuan

This paper introduces Magnus-based methods for solving stochastic delay-differential equations (SDDEs). We construct Magnus--Euler--Maruyama (MEM) and Magnus--Milstein (MM) schemes by combining stochastic Magnus integrators with Taylor…

Numerical Analysis · Mathematics 2025-06-23 Mitchell T. Griggs , Kevin Burrage , Pamela M. Burrage

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…

Numerical Analysis · Mathematics 2017-09-01 Adam Andersson , Raphael Kruse

In this paper we develop via Girsanov's transformation a perturbation argument to investigate weak convergence of Euler-Maruyama (EM) scheme for path-dependent SDEs with H\"older continuous drifts. This approach is available to other…

Probability · Mathematics 2018-09-11 Jianhai Bao , Jinghai Shao

We derive a novel variational expectation maximization approach based on truncated posterior distributions. Truncated distributions are proportional to exact posteriors within subsets of a discrete state space and equal zero otherwise. The…

Machine Learning · Statistics 2019-07-12 Jörg Lücke

Numerical methods for SDEs with irregular coefficients are intensively studied in the literature, with different types of irregularities usually being attacked separately. In this paper we combine two different types of irregularities:…

Numerical Analysis · Mathematics 2024-01-12 Kathrin Spendier , Michaela Szölgyenyi

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…

Probability · Mathematics 2013-03-07 Chaman Kumar , Sotirios Sabanis

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,…

Numerical Analysis · Mathematics 2025-01-22 Letizia Angeli , Dan Crisan , Michela Ottobre

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…

Probability · Mathematics 2011-11-18 Jianhai Bao , Chenggui Yuan

This paper is concerned with the numerical approximation of stochastic ordinary differential equations, which satisfy a global monotonicity condition. This condition includes several equations with super-linearly growing drift and diffusion…

Numerical Analysis · Mathematics 2015-10-09 Wolf-Jürgen Beyn , Elena Isaak , Raphael Kruse

In recent years tamed schemes have become an important technique for simulating SDEs and SPDEs whose continuous coefficients display superlinear growth. The taming method, which involves curbing the growth of the coefficients as a function…

Probability · Mathematics 2022-11-23 Tim Johnston , Sotirios Sabanis

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…

Probability · Mathematics 2020-11-25 Martin Hutzenthaler , Arnulf Jentzen

We study the strong approximation of stochastic differential equations with discontinuous drift coefficients and (possibly) degenerate diffusion coefficients. To account for the discontinuity of the drift coefficient we construct an…

Numerical Analysis · Mathematics 2019-04-25 Andreas Neuenkirch , Michaela Szölgyenyi , Lukasz Szpruch

In this paper we consider multidimensional stochastic differential equations (SDEs) with discontinuous drift and possibly degenerate diffusion coefficient. We prove an existence and uniqueness result for this class of SDEs and we present a…

Numerical Analysis · Mathematics 2018-12-12 Gunther Leobacher , Michaela Szölgyenyi