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Related papers: Moderate deviations via cumulants

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A moderate deviation principle as well as moderate and large deviation inequalities for a sequence of elements living inside a fixed Wiener chaos associated with an isonormal Gaussian process are shown. The conditions under which the…

Probability · Mathematics 2017-11-06 Matthias Schulte , Christoph Thaele

We analyze the dynamics of moderate fluctuations for macroscopic observables of the random field Curie Weiss model (i.e., standard Curie-Weiss model embedded in a site dependent, i.i.d. random environment). We obtain path space large…

Probability · Mathematics 2018-03-13 Francesca Collet , Richard C. Kraaij

In this paper, we prove the moderate deviations principle (MDP) for a general system of slow-fast dynamics. We provide a unified approach, based on weak convergence ideas and stochastic control arguments, that cover both the averaging and…

Probability · Mathematics 2017-06-02 Matthew R. Morse , Konstantinos Spiliopoulos

We consider the set M_n of all n-truncated power moment sequences of probability measures on [0,1]. We endow this set with the uniform probability. Picking randomly a point in M_n, we show that the upper canonical measure associated with…

Probability · Mathematics 2007-05-23 Fabrice Gamboa , Li-Vang Lozada-Chang

Consider the random walk $G_n : = g_n \ldots g_1$, $n \geq 1$, where $(g_n)_{n\geq 1}$ is a sequence of independent and identically distributed random elements with law $\mu$ on the general linear group ${\rm GL}(V)$ with $V=\mathbb R^d$.…

Probability · Mathematics 2022-09-13 Hui Xiao , Ion Grama , Quansheng Liu

We establish a large deviation principle for the smallest eigenvalue of a random matrix model composed of the sum of a GOE matrix and a diagonal matrix with an outlier. Our result generalizes and unifies previously studied cases.

Probability · Mathematics 2026-04-22 Jeanne Boursier , Alice Guionnet

We extend previous large deviations results for the randomised Heston model to the case of moderate deviations. The proofs involve the G\"artner-Ellis theorem and sharp large deviations tools.

Pricing of Securities · Quantitative Finance 2020-05-06 Antoine Jacquier , Fangwei Shi

Importance sampling has become an important tool for the computation of tail-based risk measures. Since such quantities are often determined mainly by rare events standard Monte Carlo can be inefficient and importance sampling provides a…

Probability · Mathematics 2013-06-29 Pierre Nyquist

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…

Probability · Mathematics 2016-12-28 Boris Tsirelson

We establish Cram\'er-type moderate deviation theorems for sums of locally dependent random variables and combinatorial central limit theorems. Under some mild exponential moment conditions, optimal error bounds and convergence ranges are…

Probability · Mathematics 2021-12-22 Song-Hao Liu , Zhuo-Song Zhang

Ewens-Pitman model has been successfully applied to various fields including Bayesian statistics. There are four important estimators $K_{n},M_{l,n}$,$K_{m}^{(n)},M_{l,m}^{(n)}$. In particular, $M_{1,n}, M_{1,m}^{(n)}$ are related to…

Probability · Mathematics 2018-11-20 Youzhou Zhou

In this paper, we use the framework of mod-$\phi$ convergence to prove precise large or moderate deviations for quite general sequences of real valued random variables $(X_{n})_{n \in \mathbb{N}}$, which can be lattice or non-lattice…

Probability · Mathematics 2017-02-14 Valentin Féray , Pierre-Loïc Méliot , Ashkan Nikeghbali

A moderate deviation principle for functionals, with at most quadratic growth, of moving average processes is established. The main assumptions on the moving average process are a Logarithmic Sobolev inequality for the driving random…

Probability · Mathematics 2007-06-13 Hacene Djellout , Arnaud Guillin , Liming Wu

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…

Probability · Mathematics 2012-04-17 Pierre Del Moral , Shulan Hu , Liming Wu

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…

Information Theory · Computer Science 2016-11-17 Igal Sason

What does an Erdos-Renyi graph look like when a rare event happens? This paper answers this question when p is fixed and n tends to infinity by establishing a large deviation principle under an appropriate topology. The formulation and…

Probability · Mathematics 2011-04-05 Sourav Chatterjee , S. R. S. Varadhan

This article gives an overview of the emerging literature on large deviations for random graphs. Written for the general mathematical audience, the article begins with a short introduction to the theory of large deviations. This is followed…

Probability · Mathematics 2016-04-29 Sourav Chatterjee

The purpose of this paper is to ensure the conditions of G\"artner-Ellis Theorem for evaluations of the empirical measure. We show that up-to-date conditions for ensuring the convergence to a quasi-stationary distribution can be applied…

Probability · Mathematics 2020-04-21 Aurélien Velleret

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…

Probability · Mathematics 2016-11-04 Parisa Fatheddin , Jie Xiong

In the present paper, we consider the moderate deviation principle for the plug-in estimators of a large class of diversity indices on countable alphabets, where the distribution may change with the sample size. Our results cover some of…

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