31 citations · 40 across the 5 of their papers we have counts for
7 papers
Random valuations
Andrii Ilienko, Ilya Molchanov, Tommaso Visonà
A valuation is a finitely additive function on the family of compact convex sets in . We study non-negative infinitely divisible random valuations, with particular em…
Integer-valued valuations
Andrii Ilienko, Ilya Molchanov, Tommaso Visonà
We obtain a complete characterization of planar monotone -continuous valuations taking integer values, without assuming invariance under any group of transformations. We further…
Strong limit theorems for empirical halfspace depth trimmed regions
Andrii Ilienko, Ilya Molchanov, Riccardo Turin
We study empirical variants of the halfspace (Tukey) depth of a probability measure , which are obtained by replacing with the corresponding weighted empirical measure. We p…
Limit theorems in the extended coupon collector's problem
Andrii Ilienko
We consider an extended variant of the classical coupon collector's problem with infinite number of collections. An arriving coupon is placed in the collection, , i…
Convergence of point processes associated with coupon collector's and Dixie cup problems
Andrii Ilienko
We prove that, in the coupon collector's problem, the point processes given by the times of -th arrivals for coupons of each type, centered and normalized in a proper way, conve…
Limit theorems for multidimensional renewal sets
Andrii Ilienko, Ilya Molchanov
Consider multiple sums on the -dimensional integer grid,which are generated by i.i.d.\ random variables with a positive expectation. We prove the strong law of large numbe…
Continuous counterparts of Poisson and binomial distributions and their properties
Andrii Ilienko
On the basis of integral representations of Poisson and binomial distribution functions via complete and incomplete Euler Γ- and B-functions, we introduce and discuss continuous co…