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We prove a large deviation principle for a sequence of point processes defined by Gibbs probability measures on a Polish space. This is obtained as a consequence of a more general Laplace principle for the non-normalized Gibbs measures. We…

Probability · Mathematics 2020-04-08 David García-Zelada

A parametric theory of statistical inference is developed for the moderate deviation probability zone. The new approach to the proofs is based on the Taylor series expansion of the logarithm of the likelihood ratio based on the Hellinger…

Statistics Theory · Mathematics 2026-04-28 Mikhail Ermakov

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…

Probability · Mathematics 2019-09-25 Boris Tsirelson

Let $\{{\bf \mathcal{Z}}_n:n\geq 1\}$ be a sequence of i.i.d. random probability measures. Independently, for each $n\geq 1$, let $(X_{n1},\ldots, X_{nn})$ be a random vector of positive random variables that add up to one. This paper…

Probability · Mathematics 2021-06-24 Shui Feng

In the present paper, we consider the Pearson chi-square statistic defined on a finite alphabet which is assumed to dynamically vary as the sample size increases, and establish its moderate deviation principle.

Statistics Theory · Mathematics 2025-08-19 Zhenhong Yu , Yu Miao

The aim of this paper is to give a precise asymptotic description of some eigenvalue statistics stemming from random matrix theory. More precisely, we consider random determinants of the GUE, Laguerre, Uniform Gram and Jacobi beta ensembles…

Probability · Mathematics 2017-07-25 Martina Dal Borgo , Emma Hovhannisyan , Alain Rouault

Moderate deviation principles for stochastic differential equations driven by a Poisson random measure (PRM) in finite and infinite dimensions are obtained. Proofs are based on a variational representation for expected values of positive…

Probability · Mathematics 2014-01-29 Amarjit Budhiraja , Paul Dupuis , Arnab Ganguly

In this paper, we study large and moderate deviation principles for stochastic partial differential equations (SPDEs) on metric graphs and their associated multiscale models via the weak convergence approach, providing a refined…

Probability · Mathematics 2025-09-09 Jianbo Cui , Derui Sheng

Moderate deviation principles for empirical measure processes associated with weakly interacting Markov processes are established. Two families of models are considered: the first corresponds to a system of interacting diffusions whereas…

Probability · Mathematics 2015-10-09 Amarjit Budhiraja , Ruoyu Wu

We show that for local alternatives to uniformity which are determined by a sequence of square integrable densities the moderate deviation (MD) theorem for the corresponding Neyman-Pearson statistic does not hold in the full range for all…

Statistics Theory · Mathematics 2020-03-27 Tadeusz Inglot

In this paper we prove a Large Deviation Principle for the sequence of symmetrised empirical measures $\frac{1}{n} \sum_{i=1}^{n} \delta_{(X^n_i,X^n_{\sigma_n(i)})}$ where $\sigma_n$ is a random permutation and $((X_i^n)_{1 \leq i \leq…

Probability · Mathematics 2007-09-13 José Trashorras

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…

Probability · Mathematics 2019-09-16 Boris Tsirelson

We modify the Glauber dynamics of the Curie-Weiss model with dissipation in Dai Pra, Fischer, Regoli[2013] by considering arbitrary transition rates and we analyze the phase-portrait as well as the dynamics of moderate fluctuations for…

Probability · Mathematics 2020-05-27 Francesca Collet , Richard C. Kraaij

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.

Probability · Mathematics 2020-01-17 Rachid Belfadli , Lahcen Boulanba , Mohamed Mellouk

In this paper, we obtain a large and moderate deviation principle for the law of the maximum of a random Dyck path. Our result extend the results of Chung, Kennedy, Kaigh and Khorunzhiy and Marckert.

Probability · Mathematics 2011-07-19 Termeh Kousha

The main contribution of this article is an asymptotic expression for the rate associated with moderate deviations of subgraph counts in the Erd\H{o}s-R\'enyi random graph $G(n,m)$. Our approach is based on applying Freedman's inequalities…

Combinatorics · Mathematics 2020-02-11 Christina Goldschmidt , Simon Griffiths , Alex Scott

We consider a family of positive operator valued measures associated with representations of compact connected Lie groups. For many independent copies of a single state and a tensor power representation we show that the observed probability…

Mathematical Physics · Physics 2024-09-04 Alonso Botero , Matthias Christandl , Péter Vrana

We prove a large deviations principle for the empirical law of the block sizes of a uniformly distributed non-crossing partition. As an application we obtain a variational formula for the maximum of the support of a compactly supported…

Probability · Mathematics 2011-07-04 Janosch Ortmann

We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…

Probability · Mathematics 2022-11-03 Zachary Bezemek , Konstantinos Spiliopoulos

In this paper, we consider moderate deviations for Good's coverage estimator. The moderate deviation principle and the self-normalized moderate deviation principle for Good's coverage estimator are established. The results are also applied…

Statistics Theory · Mathematics 2013-05-10 Fuqing Gao