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This work focuses on a slow-fast system perturbed by mixed fractional Brownian motion with Hurst parameter $H\in(1/2,1)$. The integral with respect to fractional Brownian motion is the generalized Riemann-Stieltjes integral and the integral…

Probability · Mathematics 2024-10-21 Yuzuru Inahama , Yong Xu , Xiaoyu Yang

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 study the large deviations of time-integrated observables of Markov diffusions that have perfectly reflecting boundaries. We discuss how the standard spectral approach to dynamical large deviations must be modified to account for such…

Statistical Mechanics · Physics 2020-08-05 Johan du Buisson , Hugo Touchette

We establish the large deviation principle (LDP) for stochastic flows of interacting Brownian motions. In particular, we consider smoothly correlated flows, coalescing flows and Brownian motion stopped at a hitting moment.

Probability · Mathematics 2009-07-21 A. A. Dorogovtsev , O. V. Ostapenko

We consider discrete time Markov chains with Polish state space. The large deviations principle for empirical measures of a Markov chain can equivalently be stated in Laplace principle form, which builds on the convex dual pair of relative…

Probability · Mathematics 2026-01-14 Stephan Eckstein

In this paper, we are concerned with multi-scale distribution dependent stochastic differential equations driven by fractional Brownian motion (with Hurst index $H>\frac12$ and standard Brownian motion, simultaneously. Our aim is to…

Probability · Mathematics 2023-06-12 Shen Gunagjun , Zhou Huan , Wu Jianglun

In this paper we study dynamic backward problems, with the computation of conditional expectations as a main objective, in a framework where the (forward) state process satisfies a Volterra type SDE, with fractional Brownian motion as a…

Probability · Mathematics 2018-10-09 Frederi Viens , Jianfeng Zhang

The large deviation properties of equilibrium (reversible) lattice gases are mathematically reasonably well understood. Much less is known in non--equilibrium, namely for non reversible systems. In this paper we consider a simple example of…

Statistical Mechanics · Physics 2015-12-18 L. Bertini , A. De Sole , D. Gabrielli , G. Jona-Lasinio , C. Landim

The Schr\"odinger bridge problem is concerned with finding a stochastic dynamical system bridging two marginal distributions that minimises a certain transportation cost. This problem, which represents a generalisation of optimal transport…

Machine Learning · Computer Science 2026-03-03 Kirill Tamogashev , Nikolay Malkin

Schr\"{o}dinger bridge is a stochastic optimal control problem to steer a given initial state density to another, subject to controlled diffusion and deadline constraints. A popular method to numerically solve the Schr\"{o}dinger bridge…

Optimization and Control · Mathematics 2023-09-14 Alexis M. H. Teter , Yongxin Chen , Abhishek Halder

In this paper, we establish large deviation principle for the strong solution of evolutionary p-Laplace equation driven by small multiplicative Brownian noise, where the weak convergence approach plays a key role. Moreover, by using…

Probability · Mathematics 2022-10-21 Kavin R , Ananta K Majee

In this work, we study a discrete Schr\"odinger bridge problem with partial marginal observations. A main difficulty compared to the classical Schr\"odinger bridge formulation is that our problem is not strictly convex and standard…

Optimization and Control · Mathematics 2026-04-08 Michele Mascherpa , Victor Molnö , Carsten Skovmose Kallesøe , Johan Karlsson

We study the dynamics and pairwise interactions of dark soliton stripes in the two-dimensional defocusing nonlinear Schr\"odinger equation. By employing a variational approach we reduce the dynamics for dark soliton stripes to a set of…

Pattern Formation and Solitons · Physics 2019-10-30 L. A. Cisneros-Ake , R. Carretero-Gonzalez , P. G. Kevrekidis

We formulate the Schr\"odinger problem for interacting particle systems in the hydrodynamical regime thus extending the standard setting of independent particles. This involves the large deviations rate function for the empirical measure…

Probability · Mathematics 2025-06-30 L. Bertini , D. Gabrielli , G. Jona-Lasinio

One-dimensional run-and-tumble processes may converge towards some localized non-equilibrium steady state when the two velocities and/or the two switching rates are space-dependent. A long dynamical trajectory can be then analyzed via the…

Statistical Mechanics · Physics 2021-08-23 Cecile Monthus

Using the weak convergence approach, we prove the large deviation principle (LDP) for solutions to quasilinear stochastic evolution equations with small Gaussian noise in the critical variational setting, a recently developed general…

Probability · Mathematics 2026-02-23 Esmée Theewis , Mark Veraar

This paper is concerned with six variational problems and their mutual connections: The quadratic Monge-Kantorovich optimal transport, the Schr\"odinger problem, Brenier's relaxed model for incompressible fluids, the so-called Br\"odinger…

Analysis of PDEs · Mathematics 2019-08-09 Aymeric Baradat , Léonard Monsaingeon

We consider the Schr\"odinger bridge problem which, given ensemble measurements of the initial and final configurations of a stochastic dynamical system and some prior knowledge on the dynamics, aims to reconstruct the "most likely"…

Machine Learning · Statistics 2026-02-04 Stephen Y. Zhang , Michael P H Stumpf

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

We consider the problem of minimizing the entropy of a law with respect to the law of a reference branching Brownian motion under density constraints at an initial and final time. We call this problem the branching Schr\"odinger problem by…

Probability · Mathematics 2021-12-14 Aymeric Baradat , Hugo Lavenant