Related papers: Large deviation for return times
We recover the Donsker-Varadhan large deviations principle (LDP) for the empirical measure of a continuous time Markov chain on a countable (finite or infinite) state space from the joint LDP for the empirical measure and the empirical flow…
We derive an annealed large deviation principle for the normalised local times of a continuous-time random walk among random conductances in a finite domain in $\Z^d$ in the spirit of Donsker-Varadhan \cite{DV75}. We work in the interesting…
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…
We give a criterion to determine the large deviation rate functions for abstract dynamical systems on towers. As an application of this criterion we show the level 2 large deviation principle for some class of smooth interval maps with…
We establish a large deviation principle for time dependent trajectories (paths) of the empirical density of $N$ particles with long range interactions, for homogeneous systems. This result extends the classical kinetic theory that leads to…
Markov processes restarted or reset at random times to a fixed state or region in space have been actively studied recently in connection with random searches, foraging, and population dynamics. Here we study the large deviations of…
In this paper, we introduce a mathematical apparatus that is relevant for understanding a dynamical system with small random perturbations and coupled with the so-called transmutation process -- where the latter jumps from one mode to…
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…
In ergodic physical systems, time-averaged quantities converge (for large times) to their ensemble-averaged values. Large deviation theory describes rare events where these time averages differ significantly from the corresponding ensemble…
We investigate the Large Deviation behavior in small time of continuous Gaussian processes. We introduce a general procedure allowing to derive Large Deviation Principles in small time starting from the well understood context of Large…
We prove large deviations principles in large time, for the Brownian occupation time in random scenery. The random scenery is constant on unit cubes, and consist of i.i.d. bounded variables, independent of the Brownian motion. This model is…
We propose a computational method for large deviation statistics of time-averaged quantities in general Markov processes. In our proposed method, we repeat a response measurement against external forces, where the forces are determined by…
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…
Given a chaotic dynamical system and a time interval in which some quantity takes an unusually large average value, what can we say of the trajectory that yields this deviation? As an example, we study the trajectories of the archetypical…
The study of chaotic systems, where rare events play a pivotal role, is essential for understanding complex dynamics due to their sensitivity to initial conditions. Recently, tools from large deviation theory, typically applied in the…
We investigate the statistics of the local time $\mathcal{T} = \int_0^T \delta(x(t)) dt$ that a run and tumble particle (RTP) $x(t)$ in one dimension spends at the origin, with or without an external drift. By relating the local time to the…
For Markov processes evolving on multiple time-scales a combination of large component scalings and averaging of rapid fluctuations can lead to useful limits for model approximation. A general approach to proving a law of large numbers to a…
This work concerns generalized backward stochastic differential equations, which are coupled with a family of reflecting diffusion processes. First of all, we establish the large deviation principle for forward stochastic differential…
The large deviations principles are established for a class of multidimensional degenerate stochastic differential equations with reflecting boundary conditions. The results include two cases where the initial conditions are adapted and…
We establish a large deviation principle for the trajectories of Wiener processes subject to random resets to the origin occurring according to a Poisson process. In addition to the pathwise large deviation principle, we identify the rate…