arXiv subjects

Youri Davydov

Publications and source records attributed to Youri Davydov.

24 records · Page 2Linked to original sources

arXiv2011

Rearrangements of gaussian fields

The monotone rearrangement of a function is the non-decreasing function with the same distribution. The convex rearrangement of a smooth function is obtained by integrating the monotone rearrangement of its derivative. This operator can be applied to regularizations of a stochastic process to measure quantities of interest in econometrics. A multivariate generalization of these operators is proposed, and the almost sure convergence of rearrangements of regularized Gaussian fields is given. For the Fractional Brownian field or the Brownian sheet approximated on a simplicial grid, it appears that the limit object depends on the orientation of the simplices.

math.PR↗

arXiv2010

Estimation of parameters of regularly varying distributions on convex cones

The objective of this paper is to extend an estimation method of parameters of the stable distributions in $\rd$ to the regularly varying tails distributions in an arbitrary cone. The consistency and the asymptotic normality of estimators are proved. The sampling method of regrouping is modified to optimize the rate of convergence of estimators.

math.PR↗

arXiv2010

On peeling procedure applied to a Poisson point process

In the focus of our attention is the asymptotic properties of the sequence of convex hulls which arise as a result of a peeling procedure applied to the convex hull generated by a Poisson point process. Processes of the considered type are tightly connected with empirical point processes and stable random vectors. Results are given about the limit shape of the convex hulls in the case of a discrete spectral measure. We give some numerical experiments to illustrate the peeling procedure for a more large class of Poisson point processes.

math.ST↗

arXiv2009

Transformations des lois multivariées avec queues régulières

Let $X$ be a random vector in $\rd$ with a regularly varying tail. We consider two transformations $\|X\|f(\frac{X}{\|X\|})$, $f: \sd\to\sd$, and $Xf(\frac{X}{\|X\|})$, $f: \sd\to \mathbb{R}_+$. Some sufficient conditions for preserving the property of regularity of the tail for this kind of transformations are given.

math.PR↗

arXiv2007

On a non-classical invariance principle

We consider the invariance principle without the classical condition of asymptotic negligibility of individual terms. More precisely, we explore the difference of the following two distributions in the space C (of continuous functions on [0,1]). The first is the distribution of the continuous piecewise linear partial-sum process generated by a sequence of independent random variables, and the second is the distribution of the similar process generated by the sequence of normal r.v.'s with the same first two moments. The novelty is that the condition of negligibility of the r.v.'s is not imposed. We establish a necessary and sufficient condition of the weak convergence of the difference mentioned to zero measure in C.

math.PR↗

arXiv2005

Strictly stable distributions on convex cones

Using the LePage representation, a strictly stable random element in a Banach space with $α\in(0,2)$ can be represented as a sum of points of a Poisson process. This point process is union-stable, i.e. the union of its two independent copies coincides in distribution with the rescaled original point process. These concepts makes sense in any convex cone, i.e. in a commutative semigroup equipped with multiplication by numbers, and lead to a construction of stable laws in general cones by means of the LePage series. The corresponding limit theorem shows that random samples (or binomial point processes) converge in distribution to the union-stable Poisson point process, and so yields a limit theorem for normalised sums of random elements with $α$-stable limit for $α\in(0,1)$. By using the technique of harmonic analysis on semigroups we characterise distributions of $α$-stable random elements and show how possible values of $α$ relate to the properties of the semigroup and the corresponding scaling operation, in particular, their distributivity properties. The approach developed in the paper not only makes it possible to handle stable distributions in rather general cones (like spaces of sets or measures), but also provides an alternative way to prove classical limit theorems and deduce the LePage representation for strictly stable random vectors in Banach spaces.

math.PR↗