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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…

Probability · Mathematics 2016-03-23 Yanting Ji , Jianhai Bao , Chenggui Yuan

In this paper, we study the self-normalized Cram\a'{e}r-type moderate deviations for centered independent random variables $X_1, X_2,...$ with $0<E |X_i|^3 <\infty$. The main results refine Theorems 1.1 and 1.2 of Wang (2011), the…

Probability · Mathematics 2017-05-19 Hailin Sang , Lin Ge

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

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…

Numerical Analysis · Mathematics 2023-11-21 Xiaotong Li , Wei Liu , Hongjiong Tian

This work deals with the Euler-Maruyama (EM) scheme for stochastic differential equations with Markovian switching (SDEwMSs). We focus on the Lp-convergence rate (p is greater than or equal to 2) of the EM method given in this paper. As far…

Numerical Analysis · Mathematics 2022-08-30 Minghui Song , Yuhang Zhang , Mingzhu Liu

Let $(X _i)_{i\geq1}$ be a stationary sequence. Denote $m=\lfloor n^\alpha \rfloor, 0< \alpha < 1,$ and $ k=\lfloor n/m \rfloor,$ where $\lfloor a \rfloor$ stands for the integer part of $a.$ Set $S_{j}^\circ = \sum_{i=1}^m X_{m(j-1)+i},…

Probability · Mathematics 2020-05-11 Xiequan Fan , Ion Grama , Quansheng Liu , Qi-Man Shao

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

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

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.…

Probability · Mathematics 2024-09-10 Zimo Hao , Khoa Lê , Chengcheng Ling

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

We establish a Cram\'er-type moderate deviation result for self-normalized sums of weakly dependent random variables, where the moment requirement is much weaker than the non-self-normalized counterpart. The range of the moderate deviation…

Statistics Theory · Mathematics 2014-09-15 Xiaohong Chen , Qi-Man Shao , Wei Biao Wu

In Stein's method, the exchangeable pair approach is commonly used to estimate the approximation errors in normal approximation. In this paper, we establish a Cram\'er-type moderate deviation theorem of normal approximation for unbounded…

Probability · Mathematics 2022-09-26 Zhuo-Song Zhang

In this paper, we investigate the convergence of the tamed Euler-Maruyama (EM) scheme for a class of neutral stochastic differential delay equations. The strong convergence results of the tamed EM scheme are presented under global and local…

Probability · Mathematics 2016-03-23 Yanting Ji , Chenggui Yuan

Most existing literature focuses on pointwise convergence (i.e., convergence at a fixed time point) of numerical solutions for Stochastic functional differential equations (SFDEs). In contrast, this paper investigates the strong segment…

Numerical Analysis · Mathematics 2026-04-24 Shounian Deng , Weiyin Fei , Banban Shi

In this paper, we study the asymptotic error distribution for a two-level irregular discretization scheme of the solution to the stochastic differential equations (SDE for short) driven by a continuous semimartingale and obtain a central…

Probability · Mathematics 2025-12-15 Yi Guo , Yuxi Guo , Hanchao Wang

We establish a Cram\'er-type moderate deviation theorem for double-index permutation statistics (DIPS). To the best of our knowledge, previous results only provided Berry-Esseen type bounds for DIPS, which cannot yield moderate deviation…

Probability · Mathematics 2026-03-27 Songhao Liu , Qiman Shao , Jingyu Xu

Exponential stability of modified truncated Euler-Maruyama method for stochastic differential equations are investigated in this paper. Sufficient conditions for the $p$-th moment and almost sure exponential stability of the given numerical…

Probability · Mathematics 2017-04-12 Guangqiang Lan , Fang Xia

In this paper, the truncated Euler-Maruyama (EM) method is employed together with the Multi-level Monte Carlo (MLMC) method to approximate the expectations of functions of solutions to stochastic differential equations (SDEs). The…

Numerical Analysis · Mathematics 2017-02-22 Qian Guo , Wei Liu , Xuerong Mao , Weijun Zhan

Recent work in dynamic causal inference introduced a class of discrete-time stochastic processes that generalize martingale difference sequences and arrays as follows: the random variates in each sequence have expectation zero given certain…

Statistics Theory · Mathematics 2025-12-05 Walter Dempsey , Easton Huch

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