Related papers: Large deviations for a damped telegraph process

The telegraph process $X(t)$, $t>0$, (Goldstein, 1951) and the geometric telegraph process $S(t) = s_0 \exp\{(\mu -\frac12\sigma^2)t + \sigma X(t)\}$ with $\mu$ a known constant and $\sigma>0$ a parameter are supposed to be observed at…

We consider a sequence of processes defined on half-line for all non negative t. We give sufficient conditions for Large Deviation Principle (LDP) to hold in the space of continuous functions with a new metric that is more sensitive to…

Shot noise processes are used in applied probability to model a variety of physical systems in, for example, teletraffic theory, insurance and risk theory and in the engineering sciences. In this work we prove a large deviation principle…

In the framework of Harnack type Dirichlet forms, we prove a large deviation principle for the asymptotics of reversible Markov processes with rate function given by the energy of the paths.

We prove that bridges of subelliptic diffusions on a compact manifold, with distinct ends, satisfy a large deviation principle in a space of Holder continuous functions, with a good rate function, when the travel time tends to 0. This leads…

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…

Large deviation theory is a branch of probability theory that is devoted to a study of the "rate" at which empirical estimates of various quantities converge to their true values. The object of study in this paper is the rate at which…

This article gives an overview of the emerging literature on large deviations for random graphs. Written for the general mathematical audience, the article begins with a short introduction to the theory of large deviations. This is followed…

We analytically evaluate the large deviation function in a simple model of classical particle transfer between two reservoirs. We illustrate how the asymptotic large time regime is reached starting from a special propagating initial…

We prove joint large deviation principle for the \emph{ empirical pair measure} and \emph{empirical locality measure} of the \emph{near intermediate} coloured random geometric graph models on $n$ points picked uniformly in a $d-$dimensional…

This paper deals with rare events in a general {interacting gas} at high temperature, by means of Large Deviations Principles. The main result is an LDP for the tagged empirical field, which features the competition of an energy term and an…

In this article we establish two fundamental results for the sublevel set persistent homology for stationary processes indexed by the positive integers. The first is a strong law of large numbers for the persistence diagram (treated as a…

We obtain several extensions of Talagrand's lower bound for the small deviation probability using metric entropy. For Gaussian processes, our investigations are focused on processes with sub-polynomial and, respectively, exponential…

In this paper, we prove a process-level, also known as level-3 large deviation principle for a very general class of simple point processes, i.e. nonlinear Hawkes process, with a rate function given by the process-level entropy, which has…

We introduce the concept of matrix liberation process, a random matrix counterpart of the liberation process in free probability, and prove a large deviation upper bound for its empirical distribution with several properties on its rate…

We provide a general framework for learning diffusion bridges that transport prior to target distributions. It includes existing diffusion models for generative modeling, but also underdamped versions with degenerate diffusion matrices,…

Classical approaches for asymptotic convergence to the global average in a distributed fashion typically assume timely and reliable exchange of information between neighboring components of a given multi-component system. These assumptions…

We prove a large deviations principle for the total spin and the number of edges under the annealed Ising measure on generalized random graphs. We also give detailed results on how the annealing over the Ising model changes the degrees of…

We study the large deviations principle for one dimensional, continuous, homogeneous, strong Markov processes that do not necessarily behave locally as a Wiener process. Any strong Markov process $X_{t}$ in $\mathbb{R}$ that is continuous…

In this paper, we study small noise asymptotics of Markov-modulated diffusion processes in the regime that the modulating Markov chain is rapidly switching. We prove the joint sample-path large deviations principle for the Markov-modulated…