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In this paper we study general nonlinear stochastic differential equations, where the usual Brownian motion is replaced by a L\'evy process. We also suppose that the coefficient multiplying the increments of this process is merely Lipschitz…

Probability · Mathematics 2007-07-19 Benjamin Jourdain , Sylvie Méléard , Wojbor Woyczynski

Consider a process satisfying a stochastic differential equation with unknown drift parameter, and suppose that discrete observations are given. It is known that a simple least squares estimator (LSE) can be consistent, but numerically…

Statistics Theory · Mathematics 2017-03-17 Yasutaka Shimizu

Euler-Maruyama method is studied to approximate stochastic differential equations driven by the symmetric $\alpha$-stable additive noise with the $\beta$ H\"older continuous drift coefficient. When $\alpha \in (1,2)$ and $\beta \in…

Numerical Analysis · Mathematics 2024-12-20 Wei Liu

This work focuses on the numerical approximations of neutral stochastic delay differential equations with their drift and diffusion coefficients growing super-linearly with respect to both delay variables and state variables. Under…

Numerical Analysis · Mathematics 2024-02-15 Jingjing Cai , Ziheng Chen , Yuanling Niu

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

We propose a new simple and explicit numerical scheme for time-homogeneous stochastic differential equations. The scheme is based on sampling increments at each time step from a skew-symmetric probability distribution, with the level of…

Probability · Mathematics 2025-07-08 Yuga Iguchi , Samuel Livingstone , Nikolas Nüsken , Giorgos Vasdekis , Rui-Yang Zhang

Let $(U_t,V_t)$ be a bivariate L\'evy process, where $V_t$ is a subordinator and $U_t$ is a L\'evy process formed by randomly weighting each jump of $V_t$ by an independent random variable $X_t$ having cdf $F$. We investigate the asymptotic…

Probability · Mathematics 2012-10-10 Peter Kevei , David M. Mason

We consider the problem of static Bayesian inference for partially observed Levy-process models. We develop a methodology which allows one to infer static parameters and some states of the process, without a bias from the…

Computation · Statistics 2022-04-01 Hamza Ruzayqat , Ajay Jasra

This paper aims to investigate the asymptotic error distribution of several numerical methods for stochastic partial differential equations (SPDEs) with multiplicative noise. Firstly, we give the limit distribution of the normalized error…

Numerical Analysis · Mathematics 2025-11-10 Jialin Hong , Diancong Jin , Xu Wang

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

We address estimation of parametric coefficients of a pure-jump L\'evy driven univariate stochastic differential equation (SDE) model, which is observed at high frequency over a fixed time period. It is known from the previous study Masuda…

Statistics Theory · Mathematics 2018-04-18 Hiroki Masuda

In this paper we study the convergence of solutions for (possibly degenerate) stochastic differential equations driven by L\'evy processes, when the coefficients converge in some appropriate sense. First, we prove, by means of a…

Probability · Mathematics 2020-07-02 Huijie Qiao

We combine the unbiased estimators in Rhee and Glynn (Operations Research: 63(5), 1026-1043, 2015) and the Heston model with stochastic interest rates. Specifically, we first develop a semi-exact log-Euler scheme for the Heston model with…

Computational Finance · Quantitative Finance 2025-11-14 Chao Zheng , Jiangtao Pan

Levy processes are widely used in financial mathematics, telecommunication, economics, queueing theory and natural sciences for modelling. A typical model is obtained by considering finite dimensional linear stochastic SISO systems driven…

Statistics Theory · Mathematics 2014-01-07 Laszlo Gerencser , Mate Manfay

We study McKean--Vlasov Stochastic Differential Equations (MV-SDEs) whose drift and diffusion coefficients are of superlinear growth in \textit{all} their variables thus also superlinear in the measure component (the meaning is specified in…

Probability · Mathematics 2025-10-21 Simran Soni , Neelima , Chaman Kumar , Goncalo dos Reis

The asymptotic error distribution of numerical methods applied to stochastic ordinary differential equations has been well studied, which characterizes the evolution pattern of the error distribution in the small step-size regime. It is…

Numerical Analysis · Mathematics 2024-11-19 Jialin Hong , Diancong Jin , Xu Wang , Guanlin Yang

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

This study focuses on approximating solutions to SDEs driven by L\'evy processes with H\"older continuous drifts using the Euler-Maruyama scheme. We derive the $L^p$-error for a broad range of driven noises, including all nondegenerate…

Probability · Mathematics 2023-04-28 Yanfang Li , Guohuan Zhao

We study the strong convergence order of the Euler-Maruyama scheme for scalar stochastic differential equations with additive noise and irregular drift. We provide a general framework for the error analysis by reducing it to a weighted…

Probability · Mathematics 2020-11-03 Andreas Neuenkirch , Michaela Szölgyenyi

This article establishes a universal robust limit theorem under a sublinear expectation framework. Under moment and consistency conditions, we show that, for $\alpha \in(1,2)$, the i.i.d. sequence \[ \left \{ \left(…

Probability · Mathematics 2022-10-31 Mingshang Hu , Lianzi Jiang , Gechun Liang , Shige Peng