Search Results - "Marynych, Alexander"
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1
Random walks with sticky barriers
Published in Modern Stochastics: Theory and Applications (01-07-2022)“…A new class of multidimensional locally perturbed random walks called random walks with sticky barriers is introduced and analyzed. The laws of large numbers…”
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2
Stable fluctuations of iterated perturbed random walks in intermediate generations of a general branching process tree
Published in Lithuanian mathematical journal (01-10-2022)“…Consider a general branching process, a.k.a. Crump–Mode–Jagers process, generated by a perturbed random walk η 1 , ξ 1 + η 2 , ξ 1 + ξ 2 + η 3 , …, where…”
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3
Arithmetic properties of multiplicative integer-valued perturbed random walks
Published in Modern Stochastics: Theory and Applications (01-03-2024)“…Let $({\xi _{1}},{\eta _{1}})$, $({\xi _{2}},{\eta _{2}}),\dots $ be independent identically distributed ${\mathbb{N}^{2}}$-valued random vectors with…”
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4
Critical branching processes in a sparse random environment
Published in Modern Stochastics: Theory and Applications (01-10-2023)“…We introduce a branching process in a sparse random environment as an intermediate model between a Galton–Watson process and a branching process in a random…”
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5
The laws of iterated and triple logarithms for extreme values of regenerative processes
Published in Modern Stochastics: Theory and Applications (01-03-2020)“…We analyze almost sure asymptotic behavior of extreme values of a regenerative process. We show that under certain conditions a properly centered and…”
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6
A functional limit theorem for random processes with immigration in the case of heavy tails
Published in Modern Stochastics: Theory and Applications (12-04-2017)“…Let $(X_{k},\xi _{k})_{k\in \mathbb{N}}$ be a sequence of independent copies of a pair $(X,\xi )$ where X is a random process with paths in the Skorokhod space…”
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7
Lah distribution: Stirling numbers, records on compositions, and convex hulls of high-dimensional random walks
Published in Probability theory and related fields (01-12-2022)“…Let ξ 1 , ξ 2 , … be a sequence of independent copies of a random vector in R d having an absolutely continuous distribution. Consider a random walk S i : = ξ…”
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8
Facial structure of strongly convex sets generated by random samples
Published in Advances in mathematics (New York. 1965) (24-02-2022)“…The K-hull of a compact set A⊆Rd, where K⊆Rd is a fixed compact convex body, is the intersection of all translates of K that contain A. A set is called…”
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9
Divisibility properties of polynomial expressions of random integers
Published in Journal of number theory (01-06-2024)“…We study divisibility properties of a set {f1(Un(s)),…,fm(Un(s))}, where f1,…,fm are polynomials in s variables over Z and Un(s) is a point picked uniformly at…”
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10
Random Sieves and Generalized Leader-election Procedures
Published in Österreichische Zeitschrift für Statistik (15-08-2023)“…A random sieve of the set of positive integers N is an infinite sequence of nested subsets N = S0 ⊃ S1 ⊃ S2 ⊃ · · · such that Sk is obtained from Sk−1 by…”
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11
Mod-φ convergence of Stirling distributions and limit theorems for zeros of their generating functions
Published in Journal of mathematical analysis and applications (01-01-2024)“…We study mod-φ convergence of several probability distributions on the set of positive integers that involve Stirling numbers of both kinds and, as a…”
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12
Random walks in the high-dimensional limit II: The crinkled subordinator
Published in Stochastic processes and their applications (01-10-2024)“…A crinkled subordinator is an ℓ2-valued random process which can be thought of as a version of the usual one-dimensional subordinator with each out of…”
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13
Cones generated by random points on half-spheres and convex hulls of Poisson point processes
Published in Probability theory and related fields (01-12-2019)“…Let U 1 , U 2 , … be random points sampled uniformly and independently from the d -dimensional upper half-sphere. We show that, as n → ∞ , the f -vector of the…”
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14
Solutions of kinetic-type equations with perturbed collisions
Published in Stochastic processes and their applications (01-05-2023)“…We study a class of kinetic-type differential equations ∂ϕt/∂t+ϕt=Q̂ϕt, where Q̂ is an inhomogeneous smoothing transform and, for every t≥0, ϕt is the…”
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15
Moderate parts in regenerative compositions: The case of regular variation
Published in Journal of mathematical analysis and applications (01-05-2021)“…A regenerative random composition of integer n is constructed by allocating n standard exponential points over a countable number of intervals, comprising the…”
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16
Multivariate Multiplicative Functions of Uniform Random Vectors in Large Integer Domains
Published in Resultate der Mathematik (01-10-2023)“…For a wide class of sequences of integer domains D n ⊂ N d , n ∈ N , we prove distributional limit theorems for F ( X 1 ( n ) , … , X d ( n ) ) , where F is a…”
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17
GENERAL EDGEWORTH EXPANSIONS WITH APPLICATIONS TO PROFILES OF RANDOM TREES
Published in The Annals of applied probability (01-12-2017)“…We prove an asymptotic Edgeworth expansion for the profiles of certain random trees including binary search trees, random recursive trees and plane-oriented…”
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18
Functional limit theorems for the number of occupied boxes in the Bernoulli sieve
Published in Stochastic processes and their applications (01-03-2017)“…The Bernoulli sieve is the infinite Karlin “balls-in-boxes” scheme with random probabilities of stick-breaking type. Assuming that the number of placed balls…”
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19
Limit theorems for discounted convergent perpetuities II
Published in Electronic journal of probability (01-01-2023)Get full text
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20
Central limit theorem for the least common multiple of a uniformly sampled m-tuple of integers
Published in Journal of number theory (01-04-2022)“…Let Bn(m) be a set picked uniformly at random among all m-elements subsets of {1,2,…,n}. We provide a pathwise construction of the collection (Bn(m))1⩽m⩽n and…”
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