Related papers: Large deviations for processes with discontinuous …

The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as…

The paper concerns itself with establishing large deviation principles for a sequence of stochastic integrals and stochastic differential equations driven by general semimartingales in infinite-dimensional settings. The class of…

We consider multiclass feedforward queueing networks with first in first out and priority service disciplines at the nodes, and class dependent deterministic routing between nodes. The random behavior of the network is constructed from…

For a class of additive processes driven by the affine recursion $X_{n+1} = A_n X_n + B_n$, we develop a sample-path large deviations principle in the $M_1'$ topology on $D [0,1]$. We allow $B_n$ to have both signs and focus on the case…

Let $\sigma(u)$, $u\in \mathbb{R}$ be an ergodic stationary Markov chain, taking a finite number of values $a_1,...,a_m$, and $b(u)=g(\sigma(u))$, where $g$ is a bounded and measurable function. We consider the diffusion type process $$…

The problem of (pathwise) large deviations for conditionally continuous Gaussian processes is investigated. The theory of large deviations for Gaussian processes is extended to the wider class of random processes -- the conditionally…

We analyze the macroscopic behavior of multi-populations randomly connected neural networks with interaction delays. Similar to cases occurring in spin glasses, we show that the sequences of empirical measures satisfy a large deviation…

We obtain large deviations theorems for nonconventional sums with underlying process being a Markov process satisfying the Doeblin condition or a dynamical system such as subshift of finite type or hyperbolic or expanding transformation.

We consider an acyclic network of single-server queues with heterogeneous processing rates. It is assumed that each queue is fed by the superposition of a large number of i.i.d. Gaussian processes with stationary increments and positive…

We study sample-path large deviations for L\'evy processes and random walks with heavy-tailed jump-size distributions that are of Weibull type. Our main results include an extended form of an LDP (large deviations principle) in the $J_1$…

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 study the problem of exponential mixing and large deviations for discrete-time Markov processes associated with a class of random dynamical systems. Under some dissipativity and regularisation hypotheses for the underlying deterministic…

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…

We derive a large deviation principle for random permutations induced by probability measures of the unit square, called permutons. These permutations are called $\mu$-random permutations. We also introduce and study a new general class of…

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…

The theory of stochastic approximations form the theoretical foundation for studying convergence properties of many popular recursive learning algorithms in statistics, machine learning and statistical physics. Large deviations for…

Our aim is to unify and extend the large deviation upper and lower bounds for the occupation times of a Markov process with $L_2$ semigroups under minimal conditions on the state space and the process trajectories; for example, no strong…

We prove the large deviation principle for the trajectory of a broad class of mean field interacting Markov jump processes via a general analytic approach based on viscosity solutions. Examples include generalized Ehrenfest models as well…

We consider a single-server queue where interarrival and service times depend linearly and randomly on customer waiting times, and establish a sample-path moderate deviation principle (MDP) for the waiting time process. The waiting times…

In this paper we investigate the statistics of large waiting times (with respect to the total waiting time) for Bernoulli processes. We determine the corresponding rate functions explicitly and prove a large deviations asymptotic. By this…