Related papers: Large deviations of Markov chains with multiple ti…

The large deviation principle on phase space is proved for a class of Markov processes known as random population dynamics with catastrophes. In the paper we study the process which corresponds to the random population dynamics with linear…

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…

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 a continuous time Markov chain on a countable state space. We prove a joint large deviation principle (LDP) of the empirical measure and current in the limit of large time interval. The proof is based on results on the joint…

We consider an irreducible continuous time Markov chain on a finite state space and with time periodic jump rates and prove the joint large deviation principle for the empirical measure and flow and the joint large deviation principle for…

In this paper we investigate the continuum limits of a class of Markov chains. The investigation of such limits is motivated by the desire to model very large networks. We show that under some conditions, a sequence of Markov chains…

The large deviations at Level 2.5 are applied to Markov processes with absorbing states in order to obtain the explicit extinction rate of metastable quasi-stationary states in terms of their empirical time-averaged density and of their…

The purpose of this paper is to ensure the conditions of G\"artner-Ellis Theorem for evaluations of the empirical measure. We show that up-to-date conditions for ensuring the convergence to a quasi-stationary distribution can be applied…

We consider the maximum entropy Markov chain inference approach to characterize the collective statistics of neuronal spike trains, focusing on the statistical properties of the inferred model. We review large deviations techniques useful…

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…

We consider the context of molecular motors modelled by a diffusion process driven by the gradient of a weakly periodic potential that depends on an internal degree of freedom. The switch of the internal state, that can freely be…

We prove a sample path Large Deviation Principle (LDP) for a class of jump processes whose rates are not uniformly Lipschitz continuous in phase space. Building on it we further establish the corresponding Wentzell-Freidlin (W-F) (infinite…

The theory of large deviations has been applied successfully in the last 30 years or so to study the properties of equilibrium systems and to put the foundations of equilibrium statistical mechanics on a clearer and more rigorous footing. A…

We establish a large deviation principle for the solutions of a class of stochastic partial differential equations with non-Lipschitz continuous coefficients. As an application, the large deviation principle is derived for super-Brownian…

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 Markov chains which are polynomially mixing, in a weak sense expressed in terms of the space of functions on which the mixing speed is controlled. In this context, we prove polynomial large and moderate deviations inequalities.…

The dynamics of one species chemical kinetics is studied. Chemical reactions are modelled by means of continuous time Markov processes whose probability distribution obeys a suitable master equation. A large deviation theory is formally…

A general theory is developed to study individual based models which are discrete in time. We begin by constructing a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are…

We formulate some simple conditions under which a Markov chain may be approximated by the solution to a differential equation, with quantifiable error probabilities. The role of a choice of coordinate functions for the Markov chain is…

Density dependent families of Markov chains, such as the stochastic models of mass-action chemical kinetics, converge for large values of the indexing parameter $N$ to deterministic systems of differential equations (Kurtz, 1970). Moreover…