Related papers: A functional large and moderate deviation principl…

The term noncentral moderate deviations is used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between the convergence in probability to a constant (governed by a reference large deviation…

The Join-the-Shortest-Queue-d routing policy is considered for a large system with $n$ servers. Moderate deviation principles (MDP) for the occupancy process and the empirical queue length process are established as $n\to \infty$. Each MDP…

We establish a sharp large deviation principle for renewal-reward processes, supposing that each renewal involves a broad-sense reward taking values in a real separable Banach space. In fact, we demonstrate a weak large deviation principle…

We consider a large class of piecewise expanding maps T of [0,1] with a neutral fixed point, and their associated Markov chain Y_i whose transition kernel is the Perron-Frobenius operator of T with respect to the absolutely continuous…

As an important tool characterizing the long time behavior of Markov processes, the Donsker-Varadhan LDP (large deviation principle) does not directly apply to distribution dependent SDEs/SPDEs since the solutions are non-Markovian. We…

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…

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 study the large deviation behaviour of the trajectories of empirical distributions of independent copies of time-homogeneous Feller processes on locally compact metric spaces. Under the condition that we can find a suitable core for the…

We prove that the long term distribution of the queue length process in an ergodic generalised Jackson network obeys the Large Deviation Principle with a deviation function given by the quasipotential. The latter is related to the unique…

It is common, when dealing with quantum processes involving a subsystem of a much larger composite closed system, to treat them as effectively memory-less (Markovian). While open systems theory tells us that non-Markovian processes should…

Let $\Xi_n \subset \mathbb R^d$, $n\ge 1$, be a sequence of finite sets and consider a $\Xi_n$-valued, irreducible, reversible, continuous-time Markov chain $(X^{(n)}_t:t\ge 0)$. Denote by $\mathscr P(\mathbb R^d) $ the set of probability…

Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data,…

In this paper, we introduce a class of processes that contains many natural examples. The interesting feature of such type processes lays on its infinite memory that allows it to record a quite ancient history. Then, using the martingale…

Big networks express various large-scale networks in many practical areas such as computer networks, internet of things, cloud computation, manufacturing systems, transportation networks, and healthcare systems. This paper analyzes such big…

The orientational memory of particles can serve as an effective measure of diffusivity, spreading, and search efficiency in complex stochastic processes. We develop a theoretical framework to describe the decay of directional correlations…

We find that multifractal scaling is a robust property of a large class of continuous stochastic processes, constructed as exponentials of long-memory processes. The long memory is characterized by a power law kernel with tail exponent…

We prove a large deviation principle for the point process associated to $k$-element connected components in $\mathbb R^d$ with respect to the connectivity radii $r_n\to\infty$. The random points are generated from a homogeneous Poisson…

Let W be the number of points in (0,t] of a stationary finite-state Markov renewal point process. We derive a bound for the total variation distance between the distribution of W and a compound Poisson distribution. For any nonnegative…

We present limit theorems for a sequence of Piecewise Deterministic Markov Processes (PDMPs) taking values in a separable Hilbert space. This class of processes provides a rigorous framework for stochastic spatial models in which discrete…

We establish a large deviation principle for the empirical measure process associated with a general class of finite-state mean field interacting particle systems with Lipschitz continuous transition rates that satisfy a certain ergodicity…