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This note presents sharp inequalities for deviation probability of a general quadratic form of a random vector \(\xiv\) with finite exponential moments. The obtained deviation bounds are similar to the case of a Gaussian random vector. The…

Probability · Mathematics 2013-02-08 Vladimir Spokoiny

We consider a class of tempered subordinators, namely a class of subordinators with one-dimensional marginal tempered distributions which belong to a family studied in [3]. The main contribution in this paper is a non-central moderate…

Probability · Mathematics 2020-11-05 Nikolai Leonenko , Claudio Macci , Barbara Pacchiarotti

Sharp large deviation results of Bahadur-Ranga Rao type are provided for the $q$-norm of random vectors distributed on the $\ell _{p}^{n}$-ball ${\mathbb{B}}^{n}_{p}$ according to the cone probability measure or the uniform distribution for…

Probability · Mathematics 2021-08-10 Tom Kaufmann

In this paper we obtain a Bernstein type inequality for a class of weakly dependent and bounded random variables. The proofs lead to a moderate deviations principle for sums of bounded random variables with exponential decay of the strong…

Probability · Mathematics 2012-02-23 Florence Merlevède , Magda Peligrad , Emmanuel Rio

We prove two Large deviations principles (LDP) in the zone of moderate deviation probabilities. First we establish LDP for the conditional distributions of moderate deviations of empirical bootstrap measures given empirical probability…

Statistics Theory · Mathematics 2014-05-22 Mikhail Ermakov

Let $X_1,X_2,...$ be independent random variables with zero means and finite variances, and let $S_n=\sum_{i=1}^nX_i$ and $V^2_n=\sum_{i=1}^nX^2_i$. A Cram\'{e}r type moderate deviation for the maximum of the self-normalized sums…

Statistics Theory · Mathematics 2013-07-24 Weidong Liu , Qi-Man Shao , Qiying Wang

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…

Probability · Mathematics 2022-07-15 Rita Giuliano , Claudio Macci

We study Sharp Large Deviations for Pearson's empirical correlation coefficients in the Spherical and Gaussian cases

Statistics Theory · Mathematics 2019-09-13 Thi Truong , Marguerite Zani

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

We consider block codes whose rate converges to the channel capacity with increasing block length at a certain speed and examine the best possible decay of the probability of error. We prove that a moderate deviation principle holds for all…

Information Theory · Computer Science 2015-03-20 Yucel Altug , Aaron B. Wagner

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

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…

Probability · Mathematics 2025-12-18 Claudio Macci , Barbara Pacchiarotti

We describe large deviations for normalized multiple iterated sums and integrals of the form $\bbS_N^{(\nu)}(t)=N^{-\nu}\sum_{0\leq k_1<...<k_\nu\leq Nt}\xi(k_1)\otimes\cdots\otimes\xi(k_\nu)$, $t\in[0,T]$ and…

Probability · Mathematics 2026-04-06 Yuri Kifer , Ofer Zeitouni

We consider a $\mathbb{R}^d$-valued branching random walk with a stationary and ergodic environment $\xi=(\xi_n)$ indexed by time $n\in\mathbb{N}$. Let $Z_n$ be the counting measure of particles of generation $n$. With the help of the…

Probability · Mathematics 2019-10-15 Chunmao Huang , Xin Wang , Xiaoqiang Wang

Let {(X_i,Y_i)}_{i=1}^n be a sequence of independent bivariate random vectors. In this paper, we establish a refined Cram\'er type moderate deviation theorem for the general self-normalized sum \sum_{i=1}^n X_i/(\sum_{i=1}^n Y_i^2)^{1/2},…

Probability · Mathematics 2021-07-29 Lan Gao , Qi-Man Shao , Jiasheng Shi

In this paper, we prove large deviations principle for the Nadaraya-Watson estimator and for the semi-recursive kernel estimator of the regression in the multidimensional case. Under suitable conditions, we show that the rate function is a…

Statistics Theory · Mathematics 2007-06-13 Abdelkader Mokkadem , Mariane Pelletier , Baba Thiam

We prove a sharp large deviation principle concerning intervals shrinking with sub-exponential speed for certain models involving the Poincar\'e map related to a Markov family for an Axiom A flow restricted to a basic set $\Lambda$…

Dynamical Systems · Mathematics 2019-02-20 Vesselin Petkov , Luchezar Stoyanov

In various disordered systems or non-equilibrium dynamical models, the large deviations of some observables have been found to display different scalings for rare values bigger or smaller than the typical value. In the present paper, we…

Statistical Mechanics · Physics 2021-05-12 Cecile Monthus

We establish a Cram\'er-type moderate deviation theorem for double-index permutation statistics (DIPS). To the best of our knowledge, previous results only provided Berry-Esseen type bounds for DIPS, which cannot yield moderate deviation…

Probability · Mathematics 2026-03-27 Songhao Liu , Qiman Shao , Jingyu Xu

One-dimensional run-and-tumble processes may converge towards some localized non-equilibrium steady state when the two velocities and/or the two switching rates are space-dependent. A long dynamical trajectory can be then analyzed via the…

Statistical Mechanics · Physics 2021-08-23 Cecile Monthus