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Related papers: Dynamical large deviations of reflected diffusions

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Ramaswami showed recently that standard Brownian motion arises as the limit of a family of Markov-modulated linear fluid processes. We pursue this analysis with a fluid approximation for Markov-modulated Brownian motion. Furthermore, we…

Probability · Mathematics 2014-07-22 Guy Latouche , Giang T. Nguyen

We prove the dynamical large deviations for a particle system in which particles may have different velocities. We assume that we have two infinite reservoirs of particles at the boundary: this is the so-called boundary driven process. The…

Probability · Mathematics 2010-06-02 Jonathan Farfan , Alexandre B. Simas , Fabio J. Valentim

In this article integro-differential Volterra equations whose convolution kernel depends on the vector variable are considered and a connection of these equations with a class of semi-Markov processes is established. The variable order…

Probability · Mathematics 2018-07-19 Mladen Savov , Bruno Toaldo

We prove the well--posedness of a dynamical perfect plasticity model under general assumptions on the stress constraint set and on the reference configuration. The problem is studied by combining both calculus of variations and hyperbolic…

Analysis of PDEs · Mathematics 2019-12-13 Jean-François Babadjian , Vito Crismale

We prove the existence of the reflected diffusion on a complex of an arbitrary size for a large class of planar simple nested fractals. Such a process is obtained as a folding projection of the free Brownian motion from the unbounded…

Probability · Mathematics 2020-01-08 Kamil Kaleta , Mariusz Olszewski , Katarzyna Pietruska-Pałuba

We have considered the underdamped motion of a Brownian particle in the presence of a correlated external random force. The force is modeled by an Ornstein-Uhlenbeck process. We investigate the fluctuations of the work done by the external…

Statistical Mechanics · Physics 2014-11-19 Arnab Pal , Sanjib Sabhapandit

We prove a Large Deviations Principle (LDP) for systems of diffusions (particles) interacting through their ranks, when the number of particles tends to infinity. We show that the limiting particle density is given by the unique solution of…

Probability · Mathematics 2017-04-05 Amir Dembo , Mykhaylo Shkolnikov , S. R. Srinivasa Varadhan , Ofer Zeitouni

We consider a multiscale system of stochastic differential equations in which the slow component is perturbed by a small fractional Brownian motion with Hurst index $H>1/2$ and the fast component is driven by an independent Brownian motion.…

Probability · Mathematics 2025-05-13 Siragan Gailus , Ioannis Gasteratos

The thermodynamic uncertainty relation, which establishes a universal trade-off between nonequilibrium current fluctuations and dissipation, has been found for various Markovian systems. However, this relation has not been revealed for…

Statistical Mechanics · Physics 2019-07-24 Tan Van Vu , Yoshihiko Hasegawa

In this paper, we study reflected differential equations driven by continuous paths with finite $p$-variation ($1\le p<2$) and $p$-rough paths ($2\le p<3$) on domains in Euclidean spaces whose boundaries may not be smooth. We define…

Probability · Mathematics 2015-04-24 Shigeki Aida

We study the inductive biases of diffusion models with a conditioning-variable, which have seen widespread application as both text-conditioned generative image models and observation-conditioned continuous control policies. We observe that…

Machine Learning · Computer Science 2025-12-23 Daniel Pfrommer , Zehao Dou , Christopher Scarvelis , Max Simchowitz , Ali Jadbabaie

Continuous Time Markov Chains, Hawkes processes and many other interesting processes can be described as solution of stochastic differential equations driven by Poisson measures. Previous works, using the Stein's method, give the…

Probability · Mathematics 2026-04-02 Eustache Besançon , Laure Coutin , Laurent Decreusefond , Pascal Moyal

The theory of large deviations has been applied successfully in the last 30 years or so to study the properties of equilibrium systems and to put the foundations of equilibrium statistical mechanics on a clearer and more rigorous footing. A…

Statistical Mechanics · Physics 2018-09-14 Hugo Touchette , Rosemary J. Harris

We study the probability of arbitrary density profiles in conserving diffusive fields which are driven by the boundaries. We demonstrate the existence of singularities in the large-deviation functional, the direct analog of the free-energy…

Statistical Mechanics · Physics 2015-10-07 Guy Bunin , Yariv Kafri , Daniel Podolsky

We consider a reflected Ornstein-Uhlenbeck process $X$ driven by a fractional Brownian motion with Hurst parameter $H\in (0, \frac12) \cup (\frac12, 1)$. Our goal is to estimate an unknown drift parameter $\alpha\in (-\infty,\infty)$ on the…

Statistics Theory · Mathematics 2015-03-24 Chihoon Lee , Jian Song

Sticky diffusion processes on bounded domains spend finite time (and finite mean time) on the lower-dimensional space given by the boundary. Once the process hits the boundary, then it starts again after a random amount of time. While on…

Probability · Mathematics 2026-05-19 Mirko D'Ovidio

We study a $d$-dimensional branching Brownian motion inside subdiffusively expanding balls, where the boundary of the ball is deactivating in the sense that once a particle hits the moving boundary, it is instantly deactivated but is…

Probability · Mathematics 2023-12-13 Mehmet Öz , Elif Aydoğan

We consider the last zero crossing time $T_{\mu,t}$ of a Brownian motion, with drift $\mu \neq 0$ in the time interval $[0, t]$. We prove the large deviation principle of $\{T_{\mu \sqrt r t} : r > 0 \}$ as $r$ tends to infinity. Moreover,…

Probability · Mathematics 2020-07-13 Francesco Iafrate , Claudio Macci

We study the convergence of the empirical distribution associated with a system of interacting kinetic particles subject to independent Brownian forcing in a finite horizon setting, using some recent progress on kinetic non-linear partial…

Probability · Mathematics 2025-11-13 Carlo Bellingeri , Fabio Coppini

We construct obliquely reflected Brownian motions in all bounded simply connected planar domains, including non-smooth domains, with general reflection vector fields on the boundary. Conformal mappings and excursion theory are our main…

Probability · Mathematics 2015-12-09 Krzysztof Burdzy , Zhen-Qing Chen , Donald Marshall , Kavita Ramanan