Related papers: Non-central moderate deviations for compound fract…

This is basically a polished presentation for Sections 1,2 of arXiv:0801.1050. The Moderate Deviations Principle (MDP) is well-understood for sums of independent random variables, worse understood for stationary random sequences, and…

This paper introduces the Generalized Fractional Compound Poisson Process (GFCPP), which claims to be a unified fractional version of the compound Poisson process (CPP) that encompasses existing variations as special cases. We derive its…

In this paper, we expand and generalize the findings presented in our previous work on the law of large numbers and the large deviation principle for Poisson processes with uniform catastrophes. We study three distinct scalings: sublinear…

Moderate deviation principle is achieved by the weak convergence approach for a stochastic Schr\"odinger type equation with linear drift term and noise driven by a $Q$-Wiener process. The central limit theorem is also shown for the equation…

In this paper, we establish a central limit theorem and a moderate deviations for 2D stochastic primitive equations with multiplicative noise. The proof is mainly based on the weak convergence approach.

This paper is focused on the moderate-deviations analysis of binary hypothesis testing. The analysis relies on a concentration inequality for discrete-parameter martingales with bounded jumps, where this inequality forms a refinement to the…

The goal of this paper is to study the Moderate Deviation Principle (MDP) for a system of stochastic reaction-diffusion equations with a time-scale separation in slow and fast components and small noise in the slow component. Based on weak…

We establish the moderate deviation principle for the solutions of a class of stochastic partial differential equations with non-Lipschitz continuous coefficients. As an application, we derive the moderate deviation principle for two…

We prove moderate deviation principles for the tagged particle position and current in one-dimensional symmetric simple exclusion processes. There is at most one particle per site. A particle jumps to one of its two neighbors at rate $1/2$,…

We derive large- and moderate-deviation results in random networks given as planar directed navigations on homogeneous Poisson point processes. In this non-Markovian routing scheme, starting from the origin, at each consecutive step a…

Functionals in geometric probability are often expressed as sums of bounded functions exhibiting exponential stabilization. Methods based on cumulant techniques and exponential modifications of measures show that such functionals satisfy…

We prove a moderate deviation principle for the continuous time interpolation of discrete time recursive stochastic processes. The methods of proof are somewhat different from the corresponding large deviation result, and in particular the…

Suppose that a compound Poisson process is observed discretely in time and assume that its jump distribution is supported on the set of natural numbers. In this paper we propose a non-parametric Bayesian approach to estimate the intensity…

Large and moderate deviation probabilities play an important role in many applied areas, such as insurance and risk analysis. This paper studies the exact moderate and large deviation asymptotics in non-logarithmic form for linear processes…

We construct a compound Poisson process conditioned on its random summation that represents the sizes of the connected components in the sparse Erd\H{o}s-R\'enyi random graph $G(n,c/n)$. This new representation depicts a connection between…

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 purpose of this paper is to investigate the deviation inequalities and the moderate deviation principle of the least squares estimators of the unknown parameters of general $p$th-order bifurcating autoregressive processes, under…

A moderate deviations principle for the law of a stochastic Burgers equation is proved via the weak convergence approach. In addition, some useful estimates toward a central limit theorem are established.

The Moderate Deviations Principle (MDP) is well-understood for sums of independent random variables, worse understood for stationary random sequences, and scantily understood for random fields. Here it is established for splittable random…

This article is concerned with moderate deviation principles of a general class of mean eld type interacting particle models. We discuss functional moderate deviations of the occupation measures for both the strong -topology on the space of…