Related papers: Moderate deviations for random fields and random c…

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…

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…

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…

By extending the methods in Peligrad et al. (2014a, b), we establish exact moderate and large deviation asymptotics for linear random fields with independent innovations. These results are useful for studying nonparametric regression with…

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 some planary random…

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.

An example of a discrete-time stationary random process whose sums follow the normal approximation within a given part of the region of moderate deviations, but violate it outside this part.

The term moderate deviations is often used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between a convergence in probability of some random variables to a constant and a weak convergence…

Precise asymptotics for moderate deviation probabilities are established for open convex sets in both the finite- and infinite-dimensional settings. Our results are based on the existence of dominating points for these sets, a related…

We prove large and moderate deviation principles for the distribution of an empirical mean conditioned by the value of the sum of discrete i.i.d. random variables. Some applications for combinatoric problems are discussed.

The random field Curie-Weiss model is derived from the classical Curie-Weiss model by replacing the deterministic global magnetic field by random local magnetic fields. This opens up a new and interestingly rich phase structure. In this…

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…

Cram\'er type moderate deviation theorems quantify the accuracy of the relative error of the normal approximation and provide theoretical justifications for many commonly used methods in statistics. In this paper, we develop a new…

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.

The term \emph{moderate deviations} is often used in the literature to mean a class of large deviation principles that, in some sense, fill the gap between a convergence in probability to zero (governed by a large deviation principle) and a…

In this paper we derive the moderate deviation principle for stationary sequences of bounded random variables under martingale-type conditions. Applications to functions of $\phi$-mixing sequences, contracting Markov chains, expanding maps…

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. An upper bound for a new class of random…

The purpose of the present paper is to establish moderate deviation principles for a rather general class of random variables fulfilling certain bounds of the cumulants. We apply a celebrated lemma of the theory of large deviations…

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 term "moderate deviations" is often used in the literature to mean a class of large deviation principles that, in some sense, fill the gap between a convergence in probability to zero (governed by a large deviation principle) and a weak…