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The aim of this paper is to study large deviations for the self-similar solution of a Kac-type kinetic equation. Under the assumption that the initial condition belongs to the domain of normal attraction of a stable law of index $\alpha <2$…
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…
We prove a large deviation principle for stochastic differential equations driven by semimartingales, with additive controls. Conditions are given in terms of characteristics of driven semimartingales, so that if the noise-control pairs…
We study large deviations and rare default clustering events in a dynamic large heterogeneous portfolio of interconnected components. Defaults come as Poisson events and the default intensities of the different components in the system…
In this paper we study the Large Deviation Principle (LDP in abbreviation) for a class of Stochastic Partial Differential Equations (SPDEs) in the whole space $\mathbb{R}^d$, with arbitrary dimension $d\geq 1$, under random influence which…
We establish large deviation principles for the largest eigenvalue of large random matrices with variance profiles. For $N \in \mathbb N$, we consider random $N \times N$ symmetric matrices $H^N$ which are such that…
A large deviation principle is established for a general class of stochastic flows in the small noise limit. This result is then applied to a Bayesian formulation of an image matching problem, and an approximate maximum likelihood property…
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…
This paper is devoted to proving the small noise asymptotic behaviour, particularly large deviation principle, for multi-scale stochastic dynamical systems with fully local monotone coefficients driven by multiplicative noise. The main…
The large deviation principle is established for the Poisson--Dirichlet distribution when the parameter $\theta$ approaches infinity. The result is then used to study the asymptotic behavior of the homozygosity and the Poisson--Dirichlet…
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.
We study a model of stochastic evolutionary game dynamics in which the probabilities that agents choose suboptimal actions are dependent on payoff consequences. We prove a sample path large deviation principle, characterizing the rate of…
The continuous time Markov process considered in this paper belongs to a class of population models with linear growth and catastrophes. There, the catastrophes happen at the arrival times of a Poisson process, and at each catastrophe time,…
We establish a large deviation principle for the occupation measure of the stochastic real Ginzburg-Landau equation driven by $\alpha$-stable noises. The proof is based on a hyper-exponential recurrence criterion. Our result indicates a…
A basic result of large deviations theory is Sanov's theorem, which states that the sequence of empirical measures of independent and identically distributed samples satisfies the large deviation principle with rate function given by…
We study the large deviations principle for locally periodic stochastic differential equations with small noise and fast oscillating coefficients. There are three possible regimes depending on how fast the intensity of the noise goes to…
The present paper is devoted to the large deviation principle (LDP), with particular emphasis on the regularity of the quasi-potential for densities of stationary and quasi-stationary distributions of randomly perturbed dynamical systems.…
The theory of large deviations constitutes a mathematical cornerstone in the foundations of Boltzmann-Gibbs statistical mechanics, based on the additive entropy $S_{BG}=- k_B\sum_{i=1}^W p_i \ln p_i$. Its optimization under appropriate…
Let $M_{l,n}$ be the number of blocks with frequency $l$ in the exchangeable random partition induced by a sample of size $n$ from the Ewens-Pitman sampling model. We show that, as $n$ tends to infinity, $n^{-1}M_{l,n}$ satisfies a large…
In the course of Darwinian evolution of a population, punctualism is an important phenomenon whereby long periods of genetic stasis alternate with short periods of rapid evolutionary change. This paper provides a mathematical interpretation…