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Related papers: Strong convergence of path sensitivities

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This paper proposes an adaptive time-stepping mothods for stochastic diffusion systems whose drift and diffusion coefficients are locally Lipschitz continuous and may exhibit polynomial growth. By controlling the growth of both the drift…

Numerical Analysis · Mathematics 2026-02-09 Xueqi Wen , Guozhen Li , Yuanping Cui , Xiaoyue Li

This paper is concerned with long-time strong approximations of SDEs with non-globally Lipschitz coefficients.Under certain non-globally Lipschitz conditions, a long-time version of fundamental strong convergence theorem is established for…

Numerical Analysis · Mathematics 2024-06-18 Xiaoming Wu , Xiaojie Wang

In this paper, we consider a class of stochastic differential equations driven by symmetric non-degenerate $\alpha$-stable processes (including cylindrical ones) with $\alpha \in (1,2)$. We first establish a quantitative estimate for the…

Probability · Mathematics 2026-04-10 Zimo Hao , Mingyan Wu

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

We study the strong $L^p$-convergence rates of the Euler-Maruyama method for stochastic differential equations driven by Brownian motion with low-regularity drift coefficients. Specifically, the drift is assumed to be in the…

Probability · Mathematics 2025-08-15 Jinlong Wei , Junhao Hu , Guangying Lv , Chenggui Yuan

We introduce an explicit, adaptive time-stepping scheme for the simulation of SPDEs with one-sided Lipschitz drift coefficients. Strong convergence rates are proven for the full space-time discretisation with multiplicative trace-class…

Numerical Analysis · Mathematics 2019-08-27 Stuart Campbell , Gabriel Lord

We give bounds for the total variation distance between the solutions to two stochastic differential equations starting at the same point and with close coefficients, which applies in particular to the distance between an exact solution and…

Probability · Mathematics 2022-12-12 Pierre Bras , Gilles Pagès , Fabien Panloup

We propose a new scheme for the long time approximation of a diffusion when the drift vector field is not globally Lipschitz. Under this assumption, regular explicit Euler scheme --with constant or decreasing step-- may explode and implicit…

Probability · Mathematics 2018-02-20 Vincent Lemaire

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

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

Consider the following stochastic differential equation driven by multiplicative noise on $\mathbb{R}^d$ with a superlinearly growing drift coefficient, \begin{align*} \mathrm{d} X_t = b (X_t) \, \mathrm{d} t + \sigma (X_t) \, \mathrm{d}…

Probability · Mathematics 2025-05-07 Xiang Li , Yingjun Mo , Haoran Yang

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

In this paper, we prove convergence rates for time discretisation schemes for semi-linear stochastic evolution equations with additive or multiplicative Gaussian noise, where the leading operator $A$ is the generator of a strongly…

Numerical Analysis · Mathematics 2024-12-19 Katharina Klioba , Mark Veraar

In this paper, we investigate the problem of strong approximation of the solutions of stochastic differential equations (SDEs) when the drift coefficient is given in integral form. We investigate its upper error bounds, in terms of the…

Numerical Analysis · Mathematics 2025-11-20 Paweł Przybyłowicz , Michał Sobieraj

The goal of this article is to establish a central limit theorem for the Euler-Maruyama scheme approximating multidimensional SDEs with elliptic Brownian diffusion, under very mild regularity requirements on the drift coefficients. When the…

Probability · Mathematics 2023-09-29 Konstantinos Dareiotis , Máté Gerencsér , Khoa Lê

This paper deals with the backward Euler method applied to semilinear parabolic stochastic partial differential equations (SPDEs) driven by additive noise. The SPDE is discretized in space by the finite element method and in time by the…

Numerical Analysis · Mathematics 2020-01-01 Jean Daniel Mukam , Antoine Tambue

In this paper, we get some convergence rates in total variation distance in approximating discretized paths of L{\'e}vy driven stochastic differential equations, assuming that the driving process is locally stable. The particular case of…

Probability · Mathematics 2022-03-08 Emmanuelle Clément

This paper analyzes a full discretization of a three-dimensional stochastic Allen-Cahn equation with multiplicative noise. The discretization combines the Euler scheme for temporal approximation and the finite element method for spatial…

Numerical Analysis · Mathematics 2024-11-27 Binjie Li , Qin Zhou

In this paper, we study weak well-posedness of a McKean-Vlasov stochastic differential equations (SDEs) whose drift is density-dependent and whose diffusion is constant. The existence part is due to H\"older stability estimates of the…

Numerical Analysis · Mathematics 2025-11-20 Anh-Dung Le

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