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We consider a one-dimensional stochastic differential equation driven by a Wiener process, where the diffusion coefficient depends on an ergodic fast process. The averaging principle is satisfied: it is well-known that the slow component…

Probability · Mathematics 2021-04-30 Charles-Edouard Bréhier

In this paper, we consider a class of nonautonomous multi-scale stochastic partial differential equations with fully local monotone coefficients. By introducing the evolution system of measures for time-inhomogeneous Markov semigroups, we…

Probability · Mathematics 2025-09-03 Mengyu Cheng , Xiaobin Sun , Yingchao Xie

We prove the averaging principle for a class of stochastic systems. The slow component is solution to a fractional differential equation, which is coupled with a fast component considered as solution to an ergodic stochastic differential…

Probability · Mathematics 2025-10-07 Charles-Edouard Bréhier , Ibrahima Faye

This work studies a two-time-scale functional system given by two jump-diffusions under the scale separation by a small parameter $\varepsilon \rightarrow 0$. The coefficients of the equations that govern the dynamics of the system depend…

Probability · Mathematics 2022-07-15 André de Oliveira Gomes , Pedro Catuogno

We study the asymptotic behavior of stochastic hyperbolic parabolic equations with slow and fast time scales. Both the strong and weak convergence in the averaging principe are established, which can be viewed as a functional law of large…

Probability · Mathematics 2020-11-12 Michael Röckner , Longjie Xie , Li Yang

The present article deals with the averaging principle for a two-time-scale system of jump-diffusion stochastic differential equation. Under suitable conditions, the weak error is expanded in powers of timescale parameter. It is proved that…

Probability · Mathematics 2018-06-01 Bengong Zhang , Hongbo Fu , Li Wan , Jicheng Liu

In the presence of multiscale dynamics in a reaction network, direct simulation methods become inefficient as they can only advance the system on the smallest scale. This work presents stochastic averaging techniques to accelerate…

Probability · Mathematics 2016-03-23 Araz Hashemi , Marcel Nunez , Petr Plechac , Dionisios G. Vlachos

This paper focuses on stochastic partial differential equations (SPDEs) under two-time-scale formulation. Distinct from the work in the existing literature, the systems are driven by $\alpha$-stable processes with $\alpha \in(1,2)$. In…

Statistics Theory · Mathematics 2016-09-30 Jianhai Bao , George Yin , Chenggui Yuan

The asymptotic behavior for fully coupled multiscale stochastic systems becomes much complicated when the fast processes do not locate in a compact space. An example is constructed to show that the averaged coefficients may become…

Probability · Mathematics 2025-09-23 Shen Wang , Jinghai Shao

In this paper, we aim to study the asymptotic behaviour for a class of McKean-Vlasov stochastic partial differential equations with slow and fast time-scales. Using the variational approach and classical Khasminskii time discretization, we…

Probability · Mathematics 2022-01-21 Wei Hong , Shihu Li , Wei Liu

This paper considers a class of nonautonomous slow-fast stochastic partial differential equations driven by $\alpha$-stable processes for $\alpha\in (1,2)$. By introducing the evolution system of measures, we establish an averaging…

Probability · Mathematics 2025-07-11 Yueling Li , Xiaobin Sun , Zijuan Wang , Yingchao Xie

The averaging principle for slow-fast systems of various kind of stochastic (partial) differential equations has been extensively studied. An analogous result was shown for slow-fast systems of rough differential equations driven by random…

Probability · Mathematics 2025-04-07 Yuzuru Inahama

In this paper, we study a system of stochastic partial differential equations with slow and fast time-scales, where the slow component is a stochastic real Ginzburg-Landau equation and the fast component is a stochastic reaction-diffusion…

Probability · Mathematics 2019-10-28 Xiaobin Sun , Jianliang Zhai

Averaging is an important method to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. This article derives an averaged equation for a class of stochastic partial differential equations without any…

Analysis of PDEs · Mathematics 2009-04-10 W. Wang , A. J. Roberts

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

We consider parametric estimation of the continuous part of a class of ergodic diffusions with jumps based on high-frequency samples. Various papers previously proposed threshold based methods, which enable us to distinguish whether…

Methodology · Statistics 2019-10-02 Hiroki Masuda , Yuma Uehara

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

This paper is devoted to studying the averaging principle for stochastic differential equations with slow and fast time-scales, where the drift coefficients satisfy local Lipschitz conditions with respect to the slow and fast variables, and…

Probability · Mathematics 2020-08-19 Wei Liu , Michael Röckner , Xiaobin Sun , Yingchao Xie

In contrast to existing works on stochastic averaging on finite intervals, we establish an averaging principle on the whole real axis, i.e. the so-called second Bogolyubov theorem, for semilinear stochastic ordinary differential equations…

Dynamical Systems · Mathematics 2020-03-27 David Cheban , Zhenxin Liu

An averaging result is proved for stochastic evolution equations with highly oscillating coefficients. This result applies in particular to equations with almost periodic coefficients. The convergence to the solution of the averaged…

Probability · Mathematics 2017-01-03 Mikhail Kamenski , Omar Mellah , Paul Raynaud de Fitte