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Featured researches published by Youri Davydov.


Bernoulli | 2011

Stability for random measures, point processes and discrete semigroups.

Youri Davydov; Ilya Molchanov; Sergei Zuyev

Discrete stability extends the classical notion of stability to random elements in discrete spaces by defining a scaling operation in a randomised way: an integer is transformed into the corresponding binomial distribution. Similarly defining the scaling operation as thinning of counting measures we characterise the corresponding discrete stability property of point processes. It is shown that these processes are exactly Cox (doubly stochastic Poisson) processes with strictly stable random intensity measures. We give spectral and LePage representations for general strictly stable random measures without assuming their independent scattering. As a consequence, spectral representations are obtained for the probability generating functional and void probabilities of discrete stable processes. An alternative cluster representation for such processes is also derived using the so-called Sibuya point processes, which constitute a new family of purely random point processes. The obtained results are then applied to explore stable random elements in discrete semigroups, where the scaling is defined by means of thinning of a point process on the basis of the semigroup. Particular examples include discrete stable vectors that generalise discrete stable random variables and the family of natural numbers with the multiplication operation, where the primes form the basis.


Statistics & Probability Letters | 2002

Convergence of generalized Lorenz curves based on stationary ergodic random sequences with deterministic noise

Youri Davydov; Ričardas Zitikis

We consider the Glivenko-Cantelli-type asymptotic behaviour of the empirical generalized Lorenz curves based on random variables forming a stationary ergodic sequence with deterministic noise. As a consequence of these results, we obtain a description of the set of limiting curves of the convexifications of stochastic processes with stationary increments and deterministic trends.


Stochastic Models | 2007

Estimating the Renewal Function When the Second Moment Is Infinite

Mark Bebbington; Youri Davydov; Ričardas Zitikis

We explore a large sample based method for determining the profile of the renewal function when the inter-renewal period does not have a finite variance. Specifically, we construct an empirical estimator and, based on it, develop confidence bands for the renewal and related functions. The estimators margin of error can be made as small as desired by choosing a sufficiently large sample size and also by considering the renewal function for sufficiently large values of its argument. For small and moderate values of the argument, we suggest using estimators available in the literature and, hence, begin with an extensive literature review on the topic.


Comptes Rendus De L Academie Des Sciences Serie I-mathematique | 2001

Principe local d'invariance pour des variables aléatoires i.i.d.

Jean-Christophe Breton; Youri Davydov

Resume Pour une suite de variables aleatoires independantes identiquement distribuees, les processus normalises constants par morceaux associes convergent faiblement vers le processus de Wiener. On renforce pour les distributions fonctionnelles la convergence pour la distance en variation pour une classe de fonctionnelles.


Sociological Methods & Research | 2018

Comparisons Between Poorest and Richest to Measure Inequality

Youri Davydov; Francesca Greselin

The observed increase in economic inequality, where the major concern is relative to the huge growth of the highest incomes, motivates to revisit classical measures of inequality and to offer new ways to synthesize the variability of the entire income distribution. The idea is to provide policy makers a way to contrast the economic position of the group of the poorer p percent of the population and to compare their mean income to the one owned by the p percent of the richest. The new measure is still a Lorenz-based one, but the significant focus is based here in equally sized and opposite parts of the population whose difference is so remarkable nowadays. We then highlight the specific information given by the new inequality measure and curve, by comparing it to the widely employed Lorenz curve and Gini index and the more recent Zenga approach, and provide an application to Italian data on household income, wealth, and consumption along the years 1980–2012. The effects of estimating inequality indices and curves from grouped data are also discussed.


Journal of Mathematical Sciences | 2016

On the Convex Hull and Winding Number of Self-Similar Processes

Youri Davydov

It is well known that for a standard Brownian motion (BM) {B(t), t ≥ 0} with values in Rd, its convex hull V (t) = conv{B(s), s ≤ t} with probability 1 for each t > 0 contains 0 as an interior point. We also know that the winding number of a typical path of a two-dimensional BM is equal to +∞. The aim of this paper is to show that these properties are not specifically “Brownian,” but hold for a much larger class of d-dimensional self-similar processes. This class contains, in particular, d-dimensional fractional Brownian motions and (concerning convex hulls) strictly stable Lévy processes. Bibliography: 10 titles.


Open Mathematics | 2014

On the asymptotic form of convex hulls of Gaussian random fields

Youri Davydov; Vygantas Paulauskas

We consider a centered Gaussian random field X = {Xt : t ∈ T} with values in a Banach space


Theory of Probability and Its Applications | 2013

A Simple Approach in Limit Theorems for Linear Random Processes and Fields with Continuous Time

Youri Davydov; Vygantas Paulauskas


Advances in Applied Probability | 2010

On the peeling procedure applied to a Poisson point process

Youri Davydov; Alexender Nagaev; Anne Philippe

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Journal of Theoretical Probability | 2009

On Asymptotic Proximity of Distributions

Youri Davydov; Vladimir Rotar

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Ričardas Zitikis

University of Western Ontario

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Vladimir Rotar

Russian Academy of Sciences

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Aude Illig

Paul Sabatier University

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