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Mean-deviation models, along with the existing theory of coherent risk measures, are well studied in the literature. In this paper, we characterize monotonic mean-deviation (risk) measures from a general mean-deviation model by applying a…

Risk Management · Quantitative Finance 2024-08-12 Xia Han , Ruodu Wang , Qinyu Wu

The law of large numbers for the empirical density for the pairs of uniformly distributed integers with a given greatest common divisor is a classic result in number theory. In this paper, we study the large deviations of the empirical…

Probability · Mathematics 2016-10-07 Behzad Mehrdad , Lingjiong Zhu

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 study large deviation properties of systems of weakly interacting particles modeled by It\^{o} stochastic differential equations (SDEs). It is known under certain conditions that the corresponding sequence of empirical measures…

Probability · Mathematics 2012-09-26 Amarjit Budhiraja , Paul Dupuis , Markus Fischer

We present two examples of a large deviations principle where the rate function is not strictly convex. This is motivated by a model used in mathematical finance (the Heston model), and adds a new item to the zoology of non strictly convex…

Probability · Mathematics 2016-04-19 Stefano De Marco , Antoine Jacquier , Patrick Roome

We consider a Markov chain on $\mathbb{R}^d$ with invariant measure $\mu$. We are interested in the rate of convergence of the empirical measures towards the invariant measure with respect to various dual distances, including in particular…

Probability · Mathematics 2022-10-13 Adrian Riekert

In this paper, we characterize the convergence of the (rescaled logarithmic) empirical spectral distribution of wavelet random matrices. We assume a moderately high-dimensional framework where the sample size $n$, the dimension $p(n)$ and,…

Probability · Mathematics 2024-01-08 Patrice Abry , Gustavo Didier , Oliver Orejola , Herwig Wendt

We consider a set of probability measures on a finite event space $\Omega$. The mutual affinity is introduced in terms of the spectrum of the associated Gram matrix. We show that, for randomly chosen measures, the empirical eigenvalue…

Mathematical Physics · Physics 2007-05-23 M. Fannes , P. Spincemaille

The paper concerns itself with establishing large deviation principles for a sequence of stochastic integrals and stochastic differential equations driven by general semimartingales in infinite-dimensional settings. The class of…

Probability · Mathematics 2017-08-25 Arnab Ganguly

The large deviations of an infinite moving average process with exponentially light tails are very similar to those of an i.i.d. sequence as long as the coefficients decay fast enough. If they do not, the large deviations change…

Probability · Mathematics 2008-02-26 Souvik Ghosh , Gennady Samorodnitsky

The aim of this paper is to develop tractable large deviation approximations for the empirical measure of a small noise diffusion. The starting point is the Freidlin-Wentzell theory, which shows how to approximate via a large deviation…

Probability · Mathematics 2021-01-11 Paul Dupuis , Guo-Jhen Wu

In this paper we define for a Bernoulli samples the \emph{ empirical infection measure}, which counts the number of positives (infections) in the Bernoulli sample and for the \emph{ pool samples} we define the empirical pool infection…

Probability · Mathematics 2020-08-25 Kwabena Doku-Amponsah

Generalized dimensions of multifractal measures are usually seen as static objects, related to the scaling properties of suitable partition functions, or moments of measures of cells. When these measures are invariant for the flow of a…

Dynamical Systems · Mathematics 2019-10-02 Théophile Caby , Davide Faranda , Giorgio Mantica , Sandro Vaienti , Pascal Yiou

We prove the Large Deviation Principle for the empirical process in a system of locally interacting Brownian motions in the nonequilibrium dynamic. Such a phenomenon has been proven only for two lattice systems: the symmetric simple…

Probability · Mathematics 2016-01-18 Insuk Seo

We consider a sequence of identically independently distributed random samples from an absolutely continuous probability measure in one dimension with unbounded density. We establish a new rate of convergence of the $\infty-$Wasserstein…

Probability · Mathematics 2018-08-03 Anning Liu , Jian-Guo Liu , Yulong Lu

We consider the general branching random walk under minimal assumptions, which in particular guarantee that the empirical particle distribution admits an almost sure central limit theorem. For such a process, we study the large time decay…

Probability · Mathematics 2017-12-07 Oren Louidor , Eliad Tsairi

The topic of this paper is the typical behavior of the spectral measures of large random matrices drawn from several ensembles of interest, including in particular matrices drawn from Haar measure on the classical Lie groups, random…

Probability · Mathematics 2013-09-16 Elizabeth S. Meckes , Mark W. Meckes

Based on recent progress in research on copula based dependence measures, we review the original Renyi's axioms on symmetric measures and propose a new set of axioms that applies to nonsymmetric measures. We show that nonsymmetric measures…

Methodology · Statistics 2015-02-16 Hui Li

We study a class of dissipative PDE's perturbed by a bounded random kick force. It is assumed that the random force is non-degenerate, so that the Markov process obtained by the restriction of solutions to integer times has a unique…

Analysis of PDEs · Mathematics 2012-12-05 Vojkan Jaksic , Vahagn Nersesyan , Claude-Alain Pillet , Armen Shirikyan

Concerning systematic effects, the recommendation given in the GUM is to correct for them, but unfortunately no detailed information is available, how to do this. This publication will show, how systematic measurement deviations can be…

Data Analysis, Statistics and Probability · Physics 2011-02-16 Michael Krystek