English
Related papers

Related papers: Large deviations for singularly interacting diffus…

200 papers

We give a new proof of the large deviation principle from the hydrodynamic limit for the Ginzberg-Landau model studied in Donsker and Varadhan (1989) using techniques from the theory of stochastic control and weak convergence methods. The…

Probability · Mathematics 2018-03-28 Sayan Banerjee , Amarjit Budhiraja , Michael Perlmutter

We establish a process level large deviation principle for systems of interacting Bessel-like diffusion processes. By establishing weak uniqueness for the limiting non-local SDE of McKean-Vlasov type, we conclude that the latter describes…

Probability · Mathematics 2013-03-14 Tomoyuki Ichiba , Mykhaylo Shkolnikov

We consider a collection of fully coupled weakly interacting diffusion processes moving in a two-scale environment. We study the moderate deviations principle of the empirical distribution of the particles' positions in the combined limit…

Probability · Mathematics 2023-07-17 Zachary Bezemek , Konstantinos Spiliopoulos

We study two problems. First, we consider the large deviation behavior of empirical measures of certain diffusion processes as, simultaneously, the time horizon becomes large and noise becomes vanishingly small. The law of large numbers…

Probability · Mathematics 2023-09-14 Amarjit Budhiraja , Pavlos Zoubouloglou

This paper is concerned with the general theme of relating the Large Deviation Principle (LDP) for the invariant measures of stochastic processes to the associated sample path LDP. It is shown that if the sample path deviation function…

Probability · Mathematics 2023-08-10 Anatolii A. Puhalskii

We prove the Large Deviation Principle for the empirical process in a system of locally interacting Brownian motions in the nonequilibrium dynamic. Such a phenomenon has been proven only for two lattice systems: the symmetric simple…

Probability · Mathematics 2016-01-18 Insuk Seo

We establish large deviation principles (LDPs) for empirical measures associated with a sequence of Gibbs distributions on $n$-particle configurations, each of which is defined in terms of an inverse temperature $% \beta_n$ and an energy…

Probability · Mathematics 2020-01-07 Paul Dupuis , Vaios Laschos , Kavita Ramanan

Moderate deviation principles for empirical measure processes associated with weakly interacting Markov processes are established. Two families of models are considered: the first corresponds to a system of interacting diffusions whereas…

Probability · Mathematics 2015-10-09 Amarjit Budhiraja , Ruoyu Wu

We show a finite-time large deviation principle (LDP) for "Dyson type" diffusion processes, including Dyson Brownian motion on the circle, for a fixed number of particles as the coupling parameter $\beta=8/\kappa$ tends to $\infty$. We also…

Probability · Mathematics 2025-08-28 Osama Abuzaid , Vivian Olsiewski Healey , Eveliina Peltola

This paper is mainly concerned with the large deviation principle of the fractional McKean-Vlasov stochastic reaction-diffusion equation defined on R^n with polynomial drift of any degree. We first prove the well-posedness of the underlying…

Probability · Mathematics 2024-06-18 Zhang Chen , Bixiang Wang

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 consider the quasi-deterministic behavior of systems with a large number, $n$, of deterministically interacting constituents. This work extends the results of a previous paper [J. Stat. Phys. 99:1225-1249 (2000)] to include vector-valued…

Statistical Mechanics · Physics 2021-04-28 Brian R. La Cour , William C. Schieve

In this paper, we prove the large deviation principle (LDP) for stochastic differential equations driven by stochastic integrals in one dimension. The result can be proved with a minimal use of rough path theory, and this implies the LDP…

Probability · Mathematics 2025-01-03 Ryoji Takano

Consider a system of $n$ weakly interacting particles driven by independent Brownian motions. In many instances, it is well known that the empirical measure converges to the solution of a partial differential equation, usually called…

Probability · Mathematics 2020-07-28 Florian Bechtold , Fabio Coppini

We consider systems of mean-field interacting diffusions, where the pairwise interaction structure is described by a sparse (and potentially inhomogeneous) random graph. Examples include the stochastic Kuramoto model with pairwise…

Probability · Mathematics 2019-09-04 Roberto I. Oliveira , Guilherme Reis

In this work we determine a process-level Large Deviation Principle (LDP) for a model of interacting particles indexed by a lattice $\mathbb{Z}^d$. The connections are random, sparse and unscaled, so that the system converges in the large…

Probability · Mathematics 2024-10-01 James MacLaurin

We study the large deviation behavior of a system of diffusing particles with a mean field interaction, described through a collection of stochastic differential equations, in which each particle is driven by a vanishing independent…

Probability · Mathematics 2021-08-10 Amarjit Budhiraja , Michael Conroy

A pathwise large deviation principle in the Wasserstein topology and a pathwise central limit theorem are proved for the empirical measure of a mean-field system of interacting diffusions. The coefficients are path-dependent. The framework…

Probability · Mathematics 2024-10-10 Louis-Pierre Chaintron

Particle approximations for certain nonlinear and nonlocal reaction-diffusion equations are studied using a system of Brownian motions with killing. The system is described by a collection of i.i.d. Brownian particles where each particle is…

Probability · Mathematics 2019-05-01 Amarjit Budhiraja , Wai-Tong Louis Fan , Ruoyu Wu

We consider a discrete-time system of n coupled random vectors, a.k.a. interacting particles. The dynamics involve a vanishing step size, some random centered perturbations, and a mean vector field which induces the coupling between the…

Probability · Mathematics 2025-06-09 Pascal Bianchi , Walid Hachem , Victor Priser