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In this paper, we proved moderate deviation principles for a fully coupled two-time-scale stochastic systems, where the slow process is given by stochastic differential equations with small noise, while the fast process is a rapidly…

Probability · Mathematics 2025-12-02 Hongjiang Qian

A large deviation principle is established for a two-scale stochastic system in which the slow component is a continuous process given by a small noise finite dimensional It\^{o} stochastic differential equation, and the fast component is a…

Probability · Mathematics 2017-05-09 Amarjit Budhiraja , Paul Dupuis , Arnab Ganguly

The purpose of this paper is to establish asymptotic behaviors of time-inhomogeneous multi-scale stochastic differential equations (SDEs). To achieve them, we analyze the evolution system of measures for time-inhomogeneous Markov…

Probability · Mathematics 2024-12-16 Xiaobin Sun , Jian Wang , Yingchao Xie

In this paper, we study the diffusion approximation for slow-fast stochastic differential equations with state-dependent switching, where the slow component $X^{\varepsilon}$ is the solution of a stochastic differential equation with…

Probability · Mathematics 2025-03-12 Xiaobin Sun , Jue Wang , Yingchao Xie

We construct a novel estimator for the diffusion coefficient of the limiting homogenized equation, when observing the slow dynamics of a multiscale model, in the case when the slow dynamics are of bounded variation. Previous research…

Statistics Theory · Mathematics 2018-07-04 Theodoros Manikas , Anastasia Papavasiliou

We present a criterion for uniform in time convergence of the weak error of the Euler scheme for Stochastic Differential equations (SDEs). The criterion requires i) exponential decay in time of the space-derivatives of the semigroup…

Probability · Mathematics 2020-07-28 D. Crisan , P. Dobson , M. Ottobre

This paper proposes a physical-statistical modeling approach for spatio-temporal data arising from a class of stochastic convection-diffusion processes. Such processes are widely found in scientific and engineering applications where…

Applications · Statistics 2020-08-07 Xiao Liu , Kyongmin Yeo , Siyuan Lu

In this paper, we develop a novel argument, the non-autonomous approximation method, to seek the asymptotic limits of the fully coupled multi-scale McKean-Vlasov stochastic systems with irregular coefficients, which, as summarized in…

Probability · Mathematics 2024-12-19 Yuewen Hou , Yun Li , Longjie Xie

Affine jump-diffusions constitute a large class of continuous-time stochastic models that are particularly popular in finance and economics due to their analytical tractability. Methods for parameter estimation for such processes require…

Mathematical Finance · Quantitative Finance 2018-11-02 Xiaowei Zhang , Peter W. Glynn

Local diffusion coefficients in disordered systems such as spin glass systems and living cells are highly heterogeneous and may change over time. Such a time-dependent and spatially heterogeneous environment results in irreproducibility of…

Statistical Mechanics · Physics 2016-12-21 Takuma Akimoto , Eiji Yamamoto

We consider a Poisson equation in $\mathbb R^d$ for the elliptic operator corresponding to an ergodic diffusion process. Optimal regularity and smoothness with respect to the parameter are obtained under mild conditions on the coefficients.…

Probability · Mathematics 2020-09-11 Michael Röckner , Longjie Xie

Consider a fast-slow system of ordinary differential equations of the form $\dot x=a(x,y)+\varepsilon^{-1}b(x,y)$, $\dot y=\varepsilon^{-2}g(y)$, where it is assumed that $b$ averages to zero under the fast flow generated by $g$. We give…

Probability · Mathematics 2017-09-01 David Kelly , Ian Melbourne

We show the propagation of regularity, uniformly in time, for the scaled solutions of the inelastic Maxwell model for small inelasticity. This result together with the weak convergence towards the homogenous cooling state present in the…

Mathematical Physics · Physics 2015-05-13 Eric A. Carlen , Jose A. Carrillo , Maria C. Carvalho

Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…

Computational Physics · Physics 2024-09-16 Elliot J. Carr

We prove pathwise large deviation principles of slow variables in slow-fast systems in the limit of time-scale separation tending to infinity. In the limit regime we consider, the convergence of the slow variable to its deterministic limit…

Probability · Mathematics 2020-11-25 Richard C. Kraaij , Mikola C. Schlottke

In the presence of quantum measurements with direct photon detection the evolution of open quantum systems is usually described by stochastic master equations with jumps. Heuristically, from these equations one can obtain diffusion models…

Mathematical Physics · Physics 2015-05-13 Clement Pellegrini , Francesco Petruccione

Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…

Machine Learning · Statistics 2026-04-28 Ludovico T. Giorgini

We study ergodic properties of a class of Markov-modulated general birth-death processes under fast regime switching. The first set of results concerns the ergodic properties of the properly scaled joint Markov process with a parameter that…

Probability · Mathematics 2019-09-17 Ari Arapostathis , Guodong Pang , Yi Zheng

We consider the long time behavior of heterogeneously interacting diffusive particle systems and their large population limit. The interaction is of mean field type with weights characterized by an underlying graphon. The limit is given by…

Probability · Mathematics 2021-04-06 Erhan Bayraktar , Ruoyu Wu

We study a large deviation principle for a system of stochastic reaction--diffusion equations (SRDEs) with a separation of fast and slow components and small noise in the slow component. The derivation of the large deviation principle is…

Probability · Mathematics 2019-05-02 Wenqing Hu , Michael Salins , Konstantinos Spiliopoulos