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Related papers: Dynamical large deviations of reflected diffusions

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We address the general problem of formulating the dynamical large deviations of non-Markovian systems in a closed form. Specifically, we consider a broad class of ``self-interacting'' jump processes whose dynamics depends on the past…

Statistical Mechanics · Physics 2026-03-25 Francesco Coghi , Amarjit Budhiraja , Juan P. Garrahan

We consider the context of molecular motors modelled by a diffusion process driven by the gradient of a weakly periodic potential that depends on an internal degree of freedom. The switch of the internal state, that can freely be…

Probability · Mathematics 2024-02-02 Serena Della Corte , Richard C. Kraaij

This work is concerned with the large deviation principle for a family of slow-fast systems perturbed by infinite-dimensional mixed fractional Brownian motion with Hurst parameter $H\in(\frac12,1)$. We adopt the weak convergence method…

Probability · Mathematics 2025-09-16 Wenting Xu , Yong Xu , Xiaoyu Yang , Bin Pei

We give new and explicitly computable examples of Gibbs-non-Gibbs transitions of mean-field type, using the large deviation approach introduced in [4]. These examples include Brownian motion with small variance and related diffusion…

Probability · Mathematics 2012-12-05 Frank Redig , Feijia Wang

The purpose of this paper is to ensure the conditions of G\"artner-Ellis Theorem for evaluations of the empirical measure. We show that up-to-date conditions for ensuring the convergence to a quasi-stationary distribution can be applied…

Probability · Mathematics 2020-04-21 Aurélien Velleret

A diffusive system coupled to unequal boundary reservoirs reaches a non-equilibrium steady state. While the full-counting-statistics of current fluctuations in these states are well understood for generic systems, results for steady-state…

Statistical Mechanics · Physics 2026-01-29 Soumyabrata Saha , Tridib Sadhu

We consider a jump-diffusion process on a bounded domain with reflection at the boundary, and establish long-term results for a general additive process of its path. This includes the long-term behaviour of its occupation time in the…

Probability · Mathematics 2022-07-29 Lea Popovic , Giovanni Zoroddu

Large deviation results are given for a class of perturbed nonhomogeneous Markov chains on finite state space which formally includes some stochastic optimization algorithms. Specifically, let {P_n} be a sequence of transition matrices on a…

Probability · Mathematics 2007-05-23 Zach Dietz , Sunder Sethuraman

We investigate the fractional diffusion approximation of a kinetic equation in the upper-half plane with diffusive reflection conditions at the boundary. In an appropriate singular limit corresponding to small Knudsen number and long time…

Analysis of PDEs · Mathematics 2019-09-04 Ludovic Cesbron , Antoine Mellet , Marjolaine Puel

A possible mechanism leading to anomalous diffusion is the presence of long-range correlations in time between the displacements of the particles. Fractional Brownian motion, a non-Markovian self-similar Gaussian process with stationary…

Statistical Mechanics · Physics 2019-04-03 Alexander H O Wada , Alex Warhover , Thomas Vojta

For a multidimensional driftless diffusion in an unbounded, smooth, sub-linear generalized parabolic domain, with oblique reflection from the boundary, we give natural conditions under which either explosion occurs, if the domain narrows…

Probability · Mathematics 2023-11-07 Mikhail V. Menshikov , Aleksandar Mijatović , Andrew R. Wade

We study the asymptotic behavior of a self-interacting one-dimensional Brownian polymer first introduced by Durrett and Rogers [Probab. Theory Related Fields 92 (1992) 337--349]. The polymer describes a stochastic process with a drift which…

Probability · Mathematics 2012-06-11 Pierre Tarrès , Bálint Tóth , Benedek Valkó

Motivated by the occurrence in rate functions of time-dependent large-deviation principles, we study a class of non-negative functions $\mathscr L$ that induce a flow, given by $\mathscr L(\rho_t,\dot\rho_t)=0$. We derive necessary and…

Functional Analysis · Mathematics 2018-01-17 Alexander Mielke , D. R. Michiel Renger , Mark A. Peletier

This paper presents a novel approach to characterize the dynamics of the limit spectrum of large random matrices. This approach is based upon the notion we call "spectral dominance". In particular, we show that the limit spectral measure…

Analysis of PDEs · Mathematics 2021-05-20 Charles Bertucci , Mérouane Debbah , Jean-Michel Lasry , Pierre-Louis Lions

The aim of this paper is to investigate the large deviations for a class of slow-fast mean-field diffusions, which extends some existing results to the case where the laws of fast process are also involved in the slow component. Due to the…

Probability · Mathematics 2026-04-28 Wei Hong , Wei Liu , Shiyuan Yang

In this paper we prove exact forms of large deviations for local times and intersection local times of fractional Brownian motions and Riemann-Liouville processes. We also show that a fractional Brownian motion and the related…

Probability · Mathematics 2010-05-31 Xia Chen , Wenbo V. Li , Jan Rosinski , Qi-Man Shao

We consider a two-dimensional Hamiltonian system perturbed by a small diffusion term, whose coefficient is state-dependent and non-degenerate. As a result, the process consists of the fast motion along the level curves and slow motion…

Probability · Mathematics 2022-05-24 Shuo Yan

Markov processes with stochastic resetting towards the origin generically converge towards non-equilibrium steady-states. Long dynamical trajectories can be thus analyzed via the large deviations at Level 2.5 for the joint probability of…

Statistical Mechanics · Physics 2021-05-07 Cecile Monthus

We exhibit a large class of Lyapunov functionals for nonlinear drift-diffusion equations with non-homogeneous Dirichlet boundary conditions. These are generalizations of large deviation functionals for underlying stochastic many-particle…

Analysis of PDEs · Mathematics 2015-06-16 T. Bodineau , J. L. Lebowitz , C. Mouhot , C. Villani

It is well-known that compositions of Markov processes with inverse subordinators are governed by integro-differential equations of generalized fractional type. This kind of processes are of wide interest in statistical physics as they are…

Probability · Mathematics 2020-05-13 Luisa Beghin , Claudio Macci , Costantino Ricciuti