Related papers: Large deviations for Dirichlet processes and Poiss…

Large deviation principles are established for the Fleming-Viot processes with neutral mutation and selection, and the corresponding equilibrium measures as the sampling rate goes to 0. All results are first proved for the finite allele…

Let L be a positive line bundle over a projective complex manifold X. Consider the space of holomorphic sections of the tensor power of order p of L. The determinant of a basis of this space, together with some given probability measure on…

We prove two Large deviations principles (LDP) in the zone of moderate deviation probabilities. First we establish LDP for the conditional distributions of moderate deviations of empirical bootstrap measures given empirical probability…

We consider the problem of learning two families of time-evolving random measures from indirect observations. In the first model, the signal is a Fleming--Viot diffusion, which is reversible with respect to the law of a Dirichlet process,…

We study the asymptotic behaviour of solutions of Forward Backward Stochastic Differential Equations in the coupled case, when the diffusion coefficient of the forward equation is multiplicatively perturbed by a small parameter that…

We study the distribution functions of several classical error terms in analytic number theory, focusing on the remainder term in the Dirichlet divisor problem $\Delta(x)$. We first bound the discrepancy between the distribution function of…

A singularly perturbed linear system of second order ordinary differential equations of reaction-diffusion type with given boundary conditions is considered. The leading term of each equation is multiplied by a small positive parameter.…

We study spatial permutations with cycle weights that are bounded or slowly diverging. We show that a phase transition occurs at an explicit critical density. The long cycles are macroscopic and their cycle lengths satisfy a…

We obtain large deviation results for a two time-scale model of jump-diffusion processes. The processes on the two time scales are fully inter-dependent, the slow process has small perturbative noise and the fast process is ergodic. Our…

Large deviation for Markov processes can be studied by Hamilton--Jacobi equation techniques. The method of proof involves three steps: First, we apply a nonlinear transform to generators of the Markov processes, and verify that limit of the…

The recently introduced two-parameter Poisson-Dirichlet diffusion extends the infinitely-many-neutral-alleles model, related to Kingman's distribution and to Fleming-Viot processes. The role of the additional parameter has been shown to…

The Large Deviation Principle is established for stochastic models defined by past-dependent non linear recursions with small noise. In the Markov case we use the result to obtain an explicit expression for the asymptotics of exit time.

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…

The Wright-Fisher diffusion is a fundamentally important model of evolution encompassing genetic drift, mutation, and natural selection. Suppose you want to infer the parameters associated with these processes from an observed sample path.…

We formulate the large deviations for a class of two scale chemical kinetic processes motivated from biological applications. The result is successfully applied to treat a genetic switching model with positive feedbacks. The corresponding…

Large deviation theory offers a powerful and general statistical framework to study the asymptotic dynamical properties of rare events. The application of the formalism to concrete experimental situations is, however, often restricted by…

In this paper, we study the large deviation principle (LDP) for two types (Type I and Type II) of multiplicative Ising models. For Types I and II, the explicit formulas for the free energy functions and the associated rate functions are…

This study focuses on large deviation principles for fully coupled multiscale multivalued stochastic systems, in which the slow component is governed by a multivalued stochastic differential equation and the fast component is described by a…

We consider the behavior of spatial point processes when subjected to a class of linear transformations indexed by a variable T. It was shown in Ellis [Adv. in Appl. Probab. 18 (1986) 646-659] that, under mild assumptions, the transformed…

In this article, we develop a framework to study the large deviation principle for matrix models and their quantized versions, by tilting the measures using the limits of spherical integrals obtained in [46,47]. As examples, we obtain 1. a…