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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…

Numerical Analysis · Mathematics 2019-03-01 Kristina Rognlien Dahl

This work develops Monte Carlo Euler adaptive time stepping methods for the weak approximation problem of jump diffusion driven stochastic differential equations. The main result is the derivation of a new expansion for the omputational…

Numerical Analysis · Mathematics 2007-05-23 E. Mordecki , A. Szepessy , R. Tempone , G. E. Zouraris

We consider the problem of the discrete-time approximation of the solution of a one-dimensional SDE with piecewise locally Lipschitz drift and continuous diffusion coefficients with polynomial growth. In this paper, we study the strong…

Numerical Analysis · Mathematics 2024-05-03 Mireille Bossy , Kerlyns Martínez

We study the estimation of time-homogeneous drift functions in multivariate stochastic differential equations with known diffusion coefficient, from multiple trajectories observed at high frequency over a fixed time horizon. We formulate…

Machine Learning · Statistics 2026-02-23 Marcos Tapia Costa , Nikolas Kantas , George Deligiannidis

An explicit numerical method is developed for a class of non-autonomous time-changed stochastic differential equations, whose coefficients obey H\"older's continuity in terms of the time variables and are allowed to grow super-linearly in…

Numerical Analysis · Mathematics 2022-05-03 Xiaotong Li , Wei Liu , Tianjiao Tang

Our subject of study is strong approximation of stochastic differential equations (SDEs) with respect to the supremum error criterion, and we seek approximations that are strongly asymptotically optimal in specific classes of…

Numerical Analysis · Mathematics 2020-07-17 Simon Hatzesberger

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…

Numerical Analysis · Mathematics 2022-08-23 Xiaoyue Li , Xuerong Mao , Guoting Song

The Euler-Maruyama scheme is known to diverge strongly and numerically weakly when applied to nonlinear stochastic differential equations (SDEs) with superlinearly growing and globally one-sided Lipschitz continuous drift coefficients.…

Probability · Mathematics 2015-03-19 Martin Hutzenthaler , Arnulf Jentzen , Peter E. Kloeden

This paper investigates the strong convergence properties of two Euler-type methods for a class of time-changed stochastic differential equations (TCSDEs) with super-linearly growing drift and diffusion coefficients. Building upon existing…

Numerical Analysis · Mathematics 2026-01-16 Shuai Wang , Yuanling Niu , Ying Zhang

Given a stochastic differential equation (SDE) in $\mathbb{R}^n$ whose solution is constrained to lie in some manifold $M \subset \mathbb{R}^n$, we propose a class of numerical schemes for the SDE whose iterates remain close to $M$ to high…

Numerical Analysis · Mathematics 2020-09-24 John Armstrong , Tim King

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…

Numerical Analysis · Mathematics 2025-05-20 Yudong Wang , Hongjiong Tian

We study the strong approximation of the solutions to singular stochastic kinetic equations (also referred to as second-order SDEs) driven by $\alpha$-stable processes, using an Euler-type scheme inspired by [11]. For these equations, the…

Probability · Mathematics 2025-11-18 Chengcheng Ling

A practical and new Runge--Kutta numerical scheme for stochastic differential equations is explored. Numerical examples demonstrate the strong convergence of the method. The first order strong convergence is then proved using Ito integrals…

Numerical Analysis · Mathematics 2012-10-04 A. J. Roberts

In this paper we consider multi-dimensional partial differential equations of parabolic type involving divergence form operators that possess a discontinuous coefficient matrix along some smooth interface. The solution of the equation is…

Probability · Mathematics 2020-03-27 Pierre Etore , Miguel Martinez

We study parameter estimation for univariate stochastic differential equations with locally Lipschitz drift and H\"older continuous multiplicative diffusion, a class commonly arising in several applications. Existing inference methods…

Methodology · Statistics 2026-05-19 Bowen Fang , Dario Spanò , Massimiliano Tamborrino

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…

Numerical Analysis · Mathematics 2025-12-10 Wei Liu , Jie Xu

The semi-implicit Euler-Maruyama (EM) method is investigated to approximate a class of time-changed stochastic differential equations, whose drift coefficient can grow super-linearly and diffusion coefficient obeys the global Lipschitz…

Numerical Analysis · Mathematics 2019-07-29 Chang-Song Deng , Wei Liu

This paper studies the numerical methods to approximate the solutions for a sort of McKean-Vlasov neutral stochastic differential delay equations (MV-NSDDEs) that the growth of the drift coefficients is super-linear. First, We obtain that…

Probability · Mathematics 2022-11-04 Yuanping Cui , Xiaoyue Li , Yi Liu , Chenggui Yuan

The truncated Euler-Maruyama (EM) method is proposed to approximate a class of non-autonomous stochastic differential equations (SDEs) with the H\"older continuity in the temporal variable and the super-linear growth in the state variable.…

Numerical Analysis · Mathematics 2019-07-19 Wei Liu , Xuerong Mao , Jingwen Tang , Yue Wu

In this paper, we first establish well-posedness results for one-dimensional McKean-Vlasov stochastic differential equations (SDEs) and related particle systems with a measure-dependent drift coefficient that is discontinuous in the spatial…

Probability · Mathematics 2024-03-29 Gunther Leobacher , Christoph Reisinger , Wolfgang Stockinger