Related papers: Convergence to the asymptotic large deviation limi…

This paper is concerned with the large deviation principle of the non-local fractional stochastic reaction-diffusion equation with a polynomial drift of arbitrary degree driven by multiplicative noise defined on unbounded domains. We first…

In many stochastic models, the observables of interest are naturally encoded in double transforms (e.g., Laplace transforms) that couple spatial and temporal variables. Notably, the double transform often provides the only analytically…

Over the last 30 years, extensive work has been devoted to developing central limit theory for partial sums of subordinated long memory linear time series. A much less studied problem, motivated by questions that are ubiquitous in extreme…

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…

What does an Erdos-Renyi graph look like when a rare event happens? This paper answers this question when p is fixed and n tends to infinity by establishing a large deviation principle under an appropriate topology. The formulation and…

For a multivariate random walk with i.i.d. jumps satisfying the Cramer moment condition and having a mean vector with at least one negative component, we derive the exact asymptotics of the probability of ever hitting the positive orthant…

We investigate the limiting behavior of discrete determinantal point processes (DPPs) towards continuous DPPs when the size of the set to sample from goes to infinity. We propose a non-asymptotic characterization of this limit in terms of…

We study maximum-likelihood-type estimation for diffusion processes when the coefficients are nonrandom and observation occurs in nonsynchronous manner. The problem of nonsynchronous observations is important when we consider the analysis…

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.

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…

Deep latent variable models learn condensed representations of data that, hopefully, reflect the inner workings of the studied phenomena. Unfortunately, these latent representations are not statistically identifiable, meaning they cannot be…

In one and two dimensions, transport coefficients may diverge in the thermodynamic limit due to long--time correlation of the corresponding currents. The effective asymptotic behaviour is addressed with reference to the problem of heat…

We investigate densities of vaguely continuous convolution semigroups of probability measures on $\mathbb{R}^d$. We expose that many typical conditions on the characteristic exponent repeatedly used in the literature of the subject are…

Transition pathways of stochastic dynamical systems are typically approximated by instantons. Here we show, using a dynamical system containing two competing pathways, that at low-to-intermediate temperatures, instantons can fail to capture…

We prove the large deviation principle for several entropy and cross entropy estimators based on return times and waiting times on shift spaces over finite alphabets. We consider shift-invariant probability measures satisfying some…

We study large deviations in the context of stochastic gradient descent for one-hidden-layer neural networks with quadratic loss. We derive a quenched large deviation principle, where we condition on an initial weight measure, and an…

For many non-equilibrium dynamics driven by small noise, in physics, chemistry, biology, or economy, rare events do matter. Large deviation theory then explains that the leading order term of the main statistical quantities have an…

We study asymptotics of fiber integrals depending on a large parameter. When the critical fiber is singular, full-asymptotic expansions are established in two different cases : local extremum and isolated real principal type singularities.…

Limit distributions for the greatest convex minorant and its derivative are considered for a general class of stochastic processes including partial sum processes and empirical processes, for independent, weakly dependent and long range…

We develop a rigorous theory of hard-sphere dynamics in the kinetic regime, away from thermal equilibrium. In the low density limit, the empirical density obeys a law of large numbers and the dynamics is governed by the Boltzmann equation.…