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This paper is the second in a series of works on weak convergence of one-step schemes for solving stochastic differential equations (SDEs) with one-sided Lipschitz conditions. It is known that the super-linear coefficients may lead to a…

Numerical Analysis · Mathematics 2024-10-29 Yuying Zhao , Xiaojie Wang , Zhongqiang Zhang

In this paper, we study a class of slow-fast stochastic partial differential equations with multiplicative Wiener noise. Under some appropriate conditions, we prove the slow component converges to the solution of the corresponding averaged…

Probability · Mathematics 2021-05-31 Yi Ge , Xiaobin Sun , Yingchao Xie

We study monotone numerical schemes for nonlocal Isaacs equations, the dynamic programming equations of stochastic differential games with jump-diffusion state processes. These equations are fully-nonlinear non-convex equations of order…

Analysis of PDEs · Mathematics 2017-09-25 Imran H. Biswas , Indranil Chowdhury , Espen R. Jakobsen

This paper studies distributed stochastic approximation algorithms based on broadcast gossip on communication networks represented by digraphs. Weak convergence of these algorithms is proved, and an associated ordinary differential equation…

Applications · Statistics 2016-09-05 Miloš S. Stanković , Nemanja Ilić , Srdjan S. Stanković

This paper is devoted to proving the strong averaging principle for slow-fast stochastic partial differential equations with locally monotone coefficients, where the slow component is a stochastic partial differential equations with locally…

Probability · Mathematics 2019-09-11 Wei Liu , Michael Röckner , Xiaobin Sun , Yingchao Xie

The reversible jump algorithm is a useful Markov chain Monte Carlo method introduced by Green (1995) that allows switches between subspaces of differing dimensionality, and therefore, model selection. Although this method is now…

Methodology · Statistics 2019-04-18 Philippe Gagnon , Mylène Bédard , Alain Desgagné

We study the asymptotic behavior for an inhomogeneous multiscale stochastic dynamical system with non-smooth coefficients. Depending on the averaging regime and the homogenization regime, two strong convergences in the averaging principle…

Probability · Mathematics 2021-04-21 Michael Röckner , Longjie Xie

In this paper, we study the averaging principle and central limit theorem for multi-scale stochastic differential equations with state-dependent switching. To accomplish this, we first study the Poisson equation associated with a Markov…

Probability · Mathematics 2023-12-19 Xiaobin Sun , Yingchao Xie

In this paper, we consider a class of slow-fast systems of stochastic partial differential equations where the nonlinearity in the slow equation is not continuous and unbounded. We first provide conditions that ensure the existence of a…

Probability · Mathematics 2023-01-02 Sandra Cerrai , Yichun Zhu

Averaging principle is an effective method for investigating dynamical systems with highly oscillating components. In this paper, we study three types of averaging principle for stochastic complex Ginzburg-Landau equations. Firstly, we…

Dynamical Systems · Mathematics 2022-11-22 Mengyu Cheng , Zhenxin Liu , Michael Röckner

Our work is part of the close link between continuous-time dissipative dynamical systems and optimization algorithms, and more precisely here, in the stochastic setting. We aim to study stochastic convex minimization problems through the…

Optimization and Control · Mathematics 2025-02-21 Rodrigo Maulen-Soto , Jalal Fadili , Hedy Attouch , Peter Ochs

One of the remarkable notions in the recent development of quantum physics is the weak value related to weak measurements. We emulate it as a two-time conditional expectation in a classical stochastic model. We use the well known…

Statistical Mechanics · Physics 2017-08-23 Hiroyuki Tomita

We study the weak finite element method solving convection-diffusion equations. A weak finite element scheme is presented based on a spacial variational form. We established a weak embedding inequality that is very useful in the weak finite…

Numerical Analysis · Mathematics 2015-06-10 Tie Zhang , Yanli Chen

We establish the existence of weak martingale solutions to a class of second order parabolic stochastic partial differential equations. The equations are driven by multiplicative jump type noise, with a non-Lipschitz multiplicative…

Probability · Mathematics 2018-09-28 Zdzisław Brzeźniak , Erika Hausenblas , Paul Razafimandimby

Stochastic averaging for a class of stochastic differential equations (SDEs) with fractional Brownian motion, of the Hurst parameter H in the interval (1/2, 1), is investigated. An averaged SDE for the original SDE is proposed, and their…

Dynamical Systems · Mathematics 2013-01-22 Yong Xu , Rong Guo , Di Liu , Huiqing Zhang , Jinqiao Duan

This article investigates weak convergence of the sequential $d$-dimensional empirical process under strong mixing. Weak convergence is established for mixing rates $\alpha_n = O(n^{-a})$, where $a>1$, which slightly improves upon existing…

Probability · Mathematics 2013-04-19 Axel Bücher

The paper estimates the rate of convergence of the weak Euler approximation for the solutions of SDEs with Hoelder continuous coefficients driven by point and martingale measures. The equation considered has a non-degenerate main part whose…

Probability · Mathematics 2010-11-23 R. Mikulevicius , C. Zhang

We consider the averaging principle for deterministic or stochastic systems with a fast stochastic component (family of continuous-time Markov chains depending on the state of the system as a parameter). We show that, due to bifurcations in…

Probability · Mathematics 2020-02-25 Mark Freidlin , Leonid Koralov

We consider in this work a system of two stochastic differential equations named the perturbed compositional gradient flow. By introducing a separation of fast and slow scales of the two equations, we show that the limit of the slow motion…

Probability · Mathematics 2018-07-26 Wenqing Hu , Chris Junchi Li

In this paper, we study a class of multiscale McKean-Vlasov stochastic systems where the entire system depends on the distribution of the fast component. First of all, by the Poisson equation method we prove that the slow component…

Probability · Mathematics 2025-09-30 Jie Xiang , Huijie Qiao