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This paper mainly investigates the strong convergence and stability of the truncated Euler-Maruyama (EM) method for stochastic differential delay equations with variable delay whose coefficients can be growing super-linearly. By…

Numerical Analysis · Mathematics 2021-08-10 Shounian Deng , Chen Fei , Weiyin Fei , Xuerong Mao

We propose a new numerical method for one dimensional stochastic differential equations (SDEs). The main idea of this method is based on a representation of a weak solution of a SDE with a time changed Brownian motion, dated back to Doeblin…

Probability · Mathematics 2020-06-05 Masaaki Fukasawa , Mitsumasa Ikeda

We consider in this work the convergence of a split-step Euler type scheme (SSM) for the numerical simulation of interacting particle Stochastic Differential Equation (SDE) systems and McKean-Vlasov Stochastic Differential Equations…

Probability · Mathematics 2023-03-28 Xingyuan Chen , Goncalo dos Reis

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

Under non-global Lipschitz condition, Euler Explicit method fails to converge strongly to the exact solution, while Euler implicit method converges but requires much computational efforts. Tamed scheme was first introduced in [2] to…

Numerical Analysis · Mathematics 2015-10-22 Antoine Tambue , Jean Daniel Mukam

In recent years, an intensive study of strong approximation of stochastic differential equations (SDEs) with a drift coefficient that may have discontinuities in space has begun. In many of these results it is assumed that the drift…

Probability · Mathematics 2021-03-01 Larisa Yaroslavtseva

We extend the taming techniques for explicit Euler approximations of stochastic differential equations (SDEs) driven by L\'evy noise with super-linearly growing drift coefficients. Strong convergence results are presented for the case of…

Probability · Mathematics 2015-01-23 Konstantinos Dareiotis , Chaman Kumar , Sotirios Sabanis

We develop and analyze a general class of Euler-type numerical schemes for Levy-driven McKean-Vlasov stochastic differential equations (SDEs), where the drift, diffusion and jump coefficients grow super-linearly in the state variable. These…

Numerical Analysis · Mathematics 2025-09-12 Jingtao Zhu , Yuying Zhao , Siqing Gan

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

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

We are investigating the first strong convergence analysis of a numerical method for stochastic differential algebraic equations (SDAEs) under a non-global Lipschitz setting. It is well known that the explicit Euler scheme fails to converge…

Numerical Analysis · Mathematics 2025-09-12 Guy Tsafack , Antoine Tambue

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

We propose an algorithm for approximating the solution of a strongly oscillating SDE, that is, a system in which some ergodic state variables evolve quickly with respect to the other variables. The algorithm profits from homogenization…

Probability · Mathematics 2015-03-19 Camilo Andrés García Trillos

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…

Numerical Analysis · Mathematics 2012-09-13 Martin Hutzenthaler , Arnulf Jentzen , Peter E. Kloeden

Existence, uniqueness, and $L_p$-approximation results are presented for scalar stochastic differential equations (SDEs) by considering the case where, the drift coefficient has finitely many spatial discontinuities while both coefficients…

Probability · Mathematics 2022-04-06 Thomas Müller-Gronbach , Sotirios Sabanis , Larisa Yaroslavtseva

In this paper, we consider scalar stochastic differential equations (SDEs) with a superlinearly growing and piecewise continuous drift coefficient. Existence and uniqueness of strong solutions of such SDEs are obtained. Furthermore, the…

Probability · Mathematics 2022-06-02 Huimin Hu , Siqing Gan

In this paper, we study the qualitative behaviour of approximation schemes for Backward Stochastic Differential Equations (BSDEs) by introducing a new notion of numerical stability. For the Euler scheme, we provide sufficient conditions in…

Probability · Mathematics 2014-07-04 Jean-François Chassagneux , Adrien Richou

We formulate a new class of stochastic partial differential equations (SPDEs), named high-order vector backward SPDEs (B-SPDEs) with jumps, which allow the high-order integral-partial differential operators into both drift and diffusion…

Probability · Mathematics 2011-05-05 Wanyang Dai

In the present article we study strong approximation of solutions of scalar stochastic differential equations (SDEs) with bounded and $\alpha$-H\"older continuous drift coefficient and constant diffusion coefficient at time point $1$.…

Probability · Mathematics 2025-04-30 Simon Ellinger , Thomas Müller-Gronbach , Larisa Yaroslavtseva

This paper introduces a randomized tamed Euler scheme tailored for L\'evy-driven stochastic differential equations (SDEs) with superlinear random coefficients and Carath\'eodory-type drift. Under assumptions that allow for time-irregular…

Numerical Analysis · Mathematics 2025-10-22 Sani Biswas , Joaquin Fontbona