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We study large deviation properties of systems of weakly interacting particles modeled by It\^{o} stochastic differential equations (SDEs). It is known under certain conditions that the corresponding sequence of empirical measures…

Probability · Mathematics 2012-09-26 Amarjit Budhiraja , Paul Dupuis , Markus Fischer

We present an error analysis of weak convergence of one-step numerical schemes for stochastic differential equations (SDEs) with super-linearly growing coefficients. Following Milstein's weak error analysis on the one-step approximation of…

Numerical Analysis · Mathematics 2023-03-29 Xiaojie Wang , Yuying Zhao , Zhongqiang Zhang

We present an error analysis of weak convergence of one-step numerical schemes for stochastic differential equations (SDEs) with super-linearly growing coefficients. Following Milstein's weak error analysis on the one-step approximation of…

Numerical Analysis · Mathematics 2023-03-29 Xiaojie Wang , Yuying Zhao , Zhongqiang Zhang

Weak approximations have been developed to calculate the expectation value of functionals of stochastic differential equations, and various numerical discretization schemes (Euler, Milshtein) have been studied by many authors. We present a…

Probability · Mathematics 2009-08-10 Hideyuki Tanaka , Arturo Kohatsu-Higa

Sticky diffusion models a Markovian particle experiencing reflection and temporary adhesion phenomena at the boundary. Numerous numerical schemes exist for approximating stopped or reflected stochastic differential equations (SDEs), but…

Numerical Analysis · Mathematics 2025-08-11 Akash Sharma

We consider the numerical approximation of the mild solution to a semilinear stochastic wave equation driven by additive noise. For the spatial approximation we consider a standard finite element method and for the temporal approximation, a…

Numerical Analysis · Mathematics 2023-12-06 Mihály Kovács , Annika Lang , Andreas Petersson

Strong convergence rates for time-discrete numerical approximations of semilinear stochastic evolution equations (SEEs) with smooth and regular nonlinearities are well understood in the literature. Weak convergence rates for time-discrete…

Probability · Mathematics 2021-11-02 Arnulf Jentzen , Ryan Kurniawan

This paper develops a new efficient scheme for approximations of expectations of the solutions to stochastic differential equations (SDEs). In particular, we present a method for connecting approximate operators based on an asymptotic…

Probability · Mathematics 2016-05-05 Akihiko Takahashi , Toshihiro Yamada

We find the weak rate of convergence of the spatially semidiscrete finite element approximation of the nonlinear stochastic heat equation. Both multiplicative and additive noise is considered under different assumptions. This extends an…

Numerical Analysis · Mathematics 2016-03-15 Adam Andersson , Stig Larsson

This paper aims at developing a systematic study for the weak rate of convergence of the Euler-Maruyama scheme for stochastic differential equations with very irregular drift and constant diffusion coefficients. We apply our method to…

Probability · Mathematics 2017-04-27 Hoang-Long Ngo , Dai Taguchi

We study the error of the Euler scheme applied to a stochastic partial differential equation. We prove that as it is often the case, the weak order of convergence is twice the strong order. A key ingredient in our proof is Malliavin…

Numerical Analysis · Mathematics 2008-12-18 Arnaud Debussche

This paper focuses on the dynamical properties of delayed complex balanced systems. We first study the relationship between the stoichiometric compatibility classes of delayed and non-delayed systems. Using this relation we give another way…

Dynamical Systems · Mathematics 2024-03-14 Xiaoyu Zhang , Tian Zhang , Chuanhou Gao

This paper provides convergence analysis for the approximation of a class of path-dependent functionals underlying a continuous stochastic process. In the first part, given a sequence of weak convergent processes, we provide a sufficient…

Probability · Mathematics 2013-07-22 Qingshuo Song , George Yin , Qing Zhang

In this paper, a weak Local Linearization scheme for Stochastic Differential Equations (SDEs) with multiplicative noise is introduced. First, for a time discretization, the solution of the SDE is locally approximated by the solution of the…

Numerical Analysis · Mathematics 2015-06-19 J. C. Jimenez , C. Mora , M. Selva

In this paper, we deal with a class of multivalued backward doubly stochastic differential equations with time delayed coefficients. Based on a slight extension of the existence and uniqueness of solutions for backward doubly stochastic…

Probability · Mathematics 2013-08-15 Wen Lu , Yong Ren , Lanying Hu

We study in this paper a weak approximation to stochastic variance reduced gradient Langevin dynamics by stochastic delay differential equations in Wasserstein-1 distance, and obtain a uniform error bound. Our approach is via a refined…

Probability · Mathematics 2021-12-21 Peng Chen , Jianya Lu , Lihu Xu

In this work we establish weak convergence rates for temporal discretisations of stochastic wave equations with multiplicative noise, in particular, for the hyperbolic Anderson model. For this class of stochastic partial differential…

Probability · Mathematics 2024-05-24 Sonja Cox , Arnulf Jentzen , Felix Lindner

It is a well-known rule of thumb that approximations of stochastic partial differential equations have essentially twice the order of weak convergence compared to the corresponding order of strong convergence. This is already known for many…

Probability · Mathematics 2016-09-28 Annika Lang

The paper studies the rate of convergence of the weak Euler approximation for solutions to SDEs driven by Levy processes, with Hoelder-continuous coefficients. It investigates the dependence of the rate on the regularity of coefficients and…

Probability · Mathematics 2013-05-14 R. Mikulevicius , C. Zhang

We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which a linear path functional of the…

Probability · Mathematics 2013-10-17 Salvatore Federico , Peter Tankov