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We experimentally investigate the transmission of light by dense atomic vapor. The light propagating in dense atomic vapor can be modeled as a L\'evy flight random walk. For such system, the step-length distribution can be modeled as…

Assume one observes independent categorical variables or, equivalently, one observes the corresponding multinomial variables. Estimating the distribution of the observed sequence amounts to estimating the expectation of the multinomial…

Statistics Theory · Mathematics 2009-06-15 C. Durot , E. Lebarbier , A. -S. Tocquet

Without measurement errors in predictors, discontinuity of a nonparametric regression function at unknown locations could be estimated using a number of existing approaches. However, it becomes a challenging problem when the predictors…

Applications · Statistics 2015-09-17 Yicheng Kang , Xiaodong Gong , Jiti Gao , Peihua Qiu

We study the problem of bivariate discrete or continuous probability density estimation under low-rank constraints.For discrete distributions, we assume that the two-dimensional array to estimate is a low-rank probability matrix. In the…

Statistics Theory · Mathematics 2024-10-23 Julien Chhor , Olga Klopp , Alexandre Tsybakov

Given a random sample extracted from a Multivariate Bernoulli Variable (MBV), we consider the problem of estimating the structure of the undirected graph for which the distribution is pairwise Markov and the parameters' vector of its…

Methodology · Statistics 2024-11-26 Daniela De Canditiis

In this paper, robust nonparametric estimators, instead of local linear estimators, are adapted for infinitesimal coefficients associated with integrated jump-diffusion models to avoid the impact of outliers on accuracy. Furthermore,…

Statistics Theory · Mathematics 2018-06-26 Yuping Song , Hanchao Wang

Multivariate elliptically-contoured distributions are widely used for modeling correlated and non-Gaussian data. In this work, we study the kurtosis of the elliptical model, which is an important parameter in many statistical analysis.…

Statistics Theory · Mathematics 2024-08-23 Bowen Zhou , Peirong Xu , Cheng Wang

Capturing the dependence structure of multivariate extreme events is a major concern in many fields involving the management of risks stemming from multiple sources, e.g. portfolio monitoring, insurance, environmental risk management and…

Machine Learning · Statistics 2016-03-15 Nicolas Goix , Anne Sabourin , Stéphan Clémençon

We investigate densities of vaguely continuous convolution semigroups of probability measures on $\mathbb{R}^d$. We expose that many typical conditions on the characteristic exponent repeatedly used in the literature of the subject are…

Probability · Mathematics 2019-07-02 Tomasz Grzywny , Karol Szczypkowski

L\'evy Flights are paradigmatic generalised random walk processes, in which the independent stationary increments---the "jump lengths"---are drawn from an $\alpha$-stable jump length distribution with long-tailed, power-law asymptote. As a…

Statistical Mechanics · Physics 2020-08-26 A. Padash , A. V. Chechkin , B. Dybiec , I. Pavlyukevich , B. Shokri , R. Metzler

The main goal of this paper is to investigate the multi-parameter stability result for a stochastic fractional differential variational inequality with L\'{e}vy jump (SFDVI with L\'{e}vy jump) under some mild conditions. We verify that…

Optimization and Control · Mathematics 2024-11-13 Yue Zeng , Yao-jia Zhang , Nan-jing Huang

We describe a framework in which is possible to develop and implement algorithms for the approximation of invariant measures of dynamical systems with a given bound on the error of the approximation. Our approach is based on a general…

Dynamical Systems · Mathematics 2017-10-05 Stefano Galatolo , Isaia Nisoli

We analyze a specific class of random systems that are driven by a symmetric L\'{e}vy stable noise. In view of the L\'{e}vy noise sensitivity to the confining "potential landscape" where jumps take place (in other words, to environmental…

Statistical Mechanics · Physics 2015-06-11 M. Zaba , P. Garbaczewski , V. Stephanovich

In various practical situations, we encounter data from stochastic processes which can be efficiently modelled by an appropriate parametric model for subsequent statistical analyses. Unfortunately, the most common estimation and inference…

Methodology · Statistics 2022-04-12 Rohan Hore , Abhik Ghosh

We consider a random walk on one-dimensional inhomogeneous graphs built from Cantor fractals. Our study is motivated by recent experiments that demonstrated superdiffusion of light in complex disordered materials, thereby termed L\'evy…

Statistical Mechanics · Physics 2011-04-19 A. Vezzani , R. Burioni , L. Caniparoli , S. Lepri

Analogue to the well-known Langevin Monte Carlo method, in this article we provide a method to sample from a target distribution \(\pi\) by simulating a solution of a stochastic differential equation. Hereby, the stochastic differential…

Probability · Mathematics 2023-03-15 David Oechsler

We study the nonparametric estimation of the jump density of a renewal reward process from one discretely observed sample path over [0,T]. We consider the regime when the sampling rate goes to 0. The main difficulty is that a renewal reward…

Statistics Theory · Mathematics 2012-07-09 Celine Duval

We study the Lp-integrated risk of some classical estimators of the density, when the observations are drawn from a strictly stationary sequence. The results apply to a large class of sequences, which can be non-mixing in the sense of…

Statistics Theory · Mathematics 2016-05-18 Jérôme Dedecker , Florence Merlevède

Up to now, the nonparametric analysis of multidimensional continuous-time Markov processes has focussed strongly on specific model choices, mostly related to symmetry of the semigroup. While this approach allows to study the performance of…

Statistics Theory · Mathematics 2022-11-04 Niklas Dexheimer , Claudia Strauch , Lukas Trottner

The multivariate extremal index function relates the asymptotic distribution of the vector of pointwise maxima of a multivariate stationary sequence to that of the independent sequence from the same stationary distribution. It also measures…

Applications · Statistics 2008-11-14 Christian Y. Robert