Related papers: Large deviations for Markov-modulated diffusion pr…
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…
We consider a mean-field system of path-dependent stochastic interacting diffusions in random media over a finite time window. The interaction term is given as a function of the empirical measure and is allowed to be non-linear and path…
The finite state semi-Markov process is a generalization over the Markov chain in which the sojourn time distribution is any general distribution. In this article we provide a sufficient stochastic maximum principle for the optimal control…
The large deviation principle is established for the distributions of a class of generalized stochastic porous media equations for both small noise and short time.
In this paper we consider the multispecies stirring process on the discrete torus. We prove a large deviation principle for the trajectory of the vector of densities of the different species. The technique of proof consists in extending the…
In the framework of Harnack type Dirichlet forms, we prove a large deviation principle for the asymptotics of reversible Markov processes with rate function given by the energy of the paths.
Time-irreversible stochastic processes are frequently used in natural sciences to explain non-equilibrium phenomena and to design efficient stochastic algorithms. Our main goal in this thesis is to analyse their dynamics by means of large…
Let $\sigma(u)$, $u\in \mathbb{R}$ be an ergodic stationary Markov chain, taking a finite number of values $a_1,...,a_m$, and $b(u)=g(\sigma(u))$, where $g$ is a bounded and measurable function. We consider the diffusion type process $$…
The main contribution of this paper is a strong converse result for $K$-hop distributed hypothesis testing against independence with multiple (intermediate) decision centers under a Markov condition. Our result shows that the set of type-II…
This paper studies the diffusion limit for a network of infinite-server queues operating under Markov modulation (meaning that the system's parameters depend on an autonomously evolving background process). In previous papers on (primarily…
We establish the large deviation principle for a topological Markov shift over infinite alphabet which satisfies strong combinatorial assumptions called ``finite irreducibility'' or ``finite primitiveness''. More precisely, we assume the…
Using the hyper-exponential recurrence criterion, a large deviation principle for the occupation measure is derived for a class of non-linear monotone stochastic partial differential equations. The main results are applied to many concrete…
We derive a large deviation principle for the density profile of occupation times of random interlacements at a fixed level in a large box of Z^d, with d bigger or equal to 3. As an application, we analyze the asymptotic behavior of the…
We consider a class of continuous time Markov chains on a compact metric space that admit an invariant measure strictly positive on open sets together with absorbing states. We prove the joint large deviation principle for the empirical…
We solve two problems related to the fluctuations of time-integrated functionals of Markov diffusions, used in physics to model nonequilibrium systems. In the first we derive and illustrate the appropriate boundary conditions on the…
Large fluctuations have received considerable attention as they encode information on the fine-scale dynamics. Large deviation relations known as fluctuation theorems also capture crucial nonequilibrium thermodynamical properties. Here we…
We prove a large deviations principle for the empirical measure of the one dimensional symmetric simple exclusion process in contact with reservoirs. The dynamics of the reservoirs is slowed down with respect to the dynamics of the system,…
We consider a diffusion given by a small noise perturbation of a dynamical system driven by a potential function with a finite number of local minima. The classical results of Freidlin and Wentzell show that the time this diffusion spends…
The large deviation principle in the small noise limit is derived for solutions of possibly degenerate It\^o stochastic differential equations with predictable coefficients, which may depend also on the large deviation parameter. The result…
We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…