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This paper establishes a discretization scheme for a large class of stochastic differential equations driven by a time-changed Brownian motion with drift, where the time change is given by a general inverse subordinator. The scheme involves…

Probability · Mathematics 2015-11-13 Ernest Jum , Kei Kobayashi

Motivated by truncated EM method introduced by Mao (2015), a new explicit numerical method named modified truncated Euler-Maruyama method is developed in this paper. Strong convergence rates of the given numerical scheme to the exact…

Probability · Mathematics 2017-01-18 Guangqiang Lan , Fang Xia

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

This paper is concerned with numerical solutions of one-dimensional SDEs with the drift being a generalised function, in particular belonging to the H\"older-Zygmund space $C^{-\gamma}$ of negative order $-\gamma<0$ in the spatial variable.…

Probability · Mathematics 2026-03-06 Luis Mario Chaparro Jáquez , Elena Issoglio , Jan Palczewski

This paper proposes an adaptive timestep construction for an Euler-Maruyama approximation of SDEs with a drift which is not globally Lipschitz. It is proved that if the timestep is bounded appropriately, then over a finite time interval the…

Numerical Analysis · Mathematics 2016-09-27 Wei Fang , Michael Bryce Giles

In this paper, the distribution dependent stochastic differential equation in a separable Hilbert space with a Dini continuous drift is investigated. The existence and uniqueness of weak and strong solutions are obtained. Moreover, some…

Probability · Mathematics 2020-04-21 Xing Huang , Yulin Song

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

We study strong approximation of $d$-dimensional stochastic differential equations (SDEs) with a discontinuous drift coefficient. More precisely, we essentially assume that the drift coefficient is piecewise Lipschitz continuous with an…

Numerical Analysis · Mathematics 2025-04-03 Thomas Müller-Gronbach , Christopher Rauhögger , Larisa Yaroslavtseva

We consider the stability problems of one dimensional SDEs when the diffusion coefficients satisfy the so called Nakao-Le Gall condition. The explicit rate of convergence of the stability problems are given by the Yamada-Watanabe method…

Probability · Mathematics 2014-04-03 Hashimoto Hashimoto , Takahiro Tsuchiya

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…

Probability · Mathematics 2022-06-24 Wei Liu , Xuerong Mao , Yue Wu

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

In this paper, we are interested in least squares estimator for a class of path-dependent McKean-Vlasov stochastic differential equations (SDEs). More precisely, we investigate the consistency and asymptotic distribution of the least…

Probability · Mathematics 2018-05-28 Panpan Ren , Jianglun Wu

This paper proposes an adaptive numerical method for stochastic delay differential equations (SDDEs) with a non-global Lipschitz drift term and a non-constant delay, building upon the work of Wei Fang and others. The method adapts the step…

Numerical Analysis · Mathematics 2024-07-02 Dongyang Liu , Minghui Song , Yuhang Zhang

In this paper, we examine the performance of randomised Euler-Maruyama (EM) method for additive time-inhomogeneous SDEs with an irregular drift driven by symmetric $\alpha$-table process, $\alpha\in (1,2)$. In particular, the drift is…

Probability · Mathematics 2025-07-16 Jianhai Bao , Haitao Wang , Yue Wu , Danqi Zhuang

In this paper, we establish the existence of weak solutions for distribution-dependent stochastic differential equations (DDSDEs) driven by a broad class of L\'{e}vy noises, where the drift coefficients satisfy specific integrability…

Probability · Mathematics 2026-04-15 Mingkun Ye

This article introduces and analyzes a new explicit, easily implementable, and full discrete accelerated exponential Euler-type approximation scheme for additive space-time white noise driven stochastic partial differential equations…

Probability · Mathematics 2020-06-04 Martin Hutzenthaler , Arnulf Jentzen , Diyora Salimova

In this paper we show the existence and uniqueness for a class of density dependent SDEs with bounded measurable drift, where the existence part is based on Euler's approximation for density dependent SDEs and the uniqueness is based on the…

Probability · Mathematics 2020-07-31 Zimo Hao , Michael Röckner , Xicheng Zhang

We consider stochastic partial differential equations under minimal assumptions: the coefficients are merely bounded and measurable and satisfy the stochastic parabolicity condition. In particular, the diffusion term is allowed to be…

Probability · Mathematics 2016-10-18 Konstantinos Dareiotis , Máté Gerencsér

In this paper, our main aim is to investigate the strong convergence for a neutral McKean-Vlasov stochastic differential equation with super-linear delay driven by fractional Brownian motion with Hurst exponent $H\in(1/2, 1)$. After giving…

Numerical Analysis · Mathematics 2024-10-01 Shengrong Wang , Jie Xie , Li Tan

We discuss numerical approximation methods for Random Time Change equations which possess a deterministic drift part and jump with state-dependent rates. It is first established that solutions to such equations are versions of certain…

Probability · Mathematics 2013-10-03 Martin G. Riedler , Girolama Notarangelo