Publications

Books

  1. Locally perturbed random walks (with A. Iksanov, A. Pilipenko and I. Samoilenko), Birkhäuser Cham, Series “Frontiers in Mathematics”, 248 p.

Submitted

  1. Multinomial random combinatorial structures and r-versions of Stirling, Eulerian and Lah numbers (with A. Iksanov, Z. Kabluchko and V. Wachtel), submitted.
  2. Almost periodic stochastic processes with applications to analytic number theory (with A. Iksanov  and Z. Kabluchko), submitted.
  3. Zeros and exponential profiles of polynomials I: Limit distributions, finite free convolutions and repeated differentiation (with J. Jalowy, Z. Kabluchko), submitted.

2025

  1. Convolution powers of unbounded measures on the positive half-life (with D. Buraczewski and A. Iksanov), Journal of Mathematical Analysis and Applications, 546, no. 2, 129232.
  2. Set-valued recursions arising from vantage-point trees (with C. Dong and I. Molchanov), to appear in Discrete and Computational Geometry.
  3. Generalised convexity with respect to families of affine maps (with Z. Kabluchko and I. Molchanov), to appear in Israel Journal of Mathematics.

2024

  1. Random walks in the high-dimensional limit I: The Wiener Spiral (with Z. Kabluchko), Ann. Inst. H. Poincaré Probab. Statist., 60, no. 4, 2945-2974.
  2. Random walks in the high-dimensional limit II: The Crinkled Subordinator (with Z. Kabluchko and K. Raschel),  Stochastic Processes and Their Applications, 176, 104428.
  3. Records in the Infinite Occupancy Scheme (with Z. Derbazi and A. Gnedin), ALEA – Latin American Journal of Probability and Statistics, 21, 1475–1493.
  4. Divisibility properties of polynomial expressions of random integers (with Z. Kabluchko), Journal of Number Theory, 259, 357–377.
  5. Mod-phi convergence of Stirling distributions and limit theorem for zeros of their generating functions (with Z. Kabluchko and H. Pitters), Journal of Mathematical Analysis and Applications, 529, no. 1, 127571.
  6. Arithmetic properties of multiplicative integer-valued perturbed random walks (with V. Bohdanskyi, V. Bohun and I. Samoilenko), Modern Stochastics: Theory and Applications, 11, no. 2, 133–148.

2023

  1. Limit theorems for discounted convergent perpetuities II (with A. Iksanov and A. Nikitin),  Electronic Journal of Probability, 28, paper no. 15.
  2. Solutions of kinetic-type equations with perturbed collisions (with D. Buraczewski and P. Dyszewski),  Stochastic Processes and Their Applications, 159, 199–224.
  3. Multivariate multiplicative functions of uniform random vectors in large integer domain (with Z. Kabluchko and K. Raschel), Results in Mathematics, 78, article no. 201.
  4. Critical branching processes in a sparse random environment (with D. Buraczewski, A. Iksanov and C. Dong), Modern Stochastics: Theory and Applications, 10, 397–411.
  5. Limit theorem for random Dirichlet series (with D. Buraczewski, A. Iksanov and C. Dong), Stochastic Processes and Their Applications, 165, 246-274.
  6. When does the chaos in the Curie-Weiss model stop to propagate? (with J. Jalowy, Z. Kabluchko and M. Löwe), Electronic Journal of Probability, 28, paper no. 139.

  7. Random sieves and generalized leader-election procedures (with C. Dong and V. Melnykov), Austrian Journal of Statistics, 52, 13-25.

2022

  1. Renewal theory for iterated perturbed random walks on a general branching process tree: intermediate generations (with V.Bogun, A. Iksanov and B. Rashytov), Journal of Applied Probability, 59, no. 2, 421-446.
  2. Facial structure of strongly convex sets generated by random samples (with I. Molchanov), Advances in Mathematics, 395, 108086.
  3. On intermediate levels of nested occupancy scheme in random environment generated by stick-breaking II (with A. Iksanov and I. Samoilenko), Stochastics, 94, no. 7., 1077-1101.
  4. Central limit theorem for the least common multiple of a uniformly sampled m-tuple of integers (with D. Buraczewski and A. Iksanov), Journal of Number Theory, 233, 301-336.
  5. Random walks with stcky barriers (with V. Bohun), Modern Stochastics: Theory and Applications, 9, no 3, 245–263.
  6. Asymptotics of arithmetic functions of GCD and LCM of random integers in hyperbolic regions (with A. Iksanov and K. Raschel), Results in Mathematics, 77, Article number: 165
  7. Lah distribution: Stirling numbers, records on compositions, and convex hulls of high-dimensional random walks (with Z. Kabluchko), Probability Theory and Related Fields,  184, no. 3-4, 969–1028.
  8. Stable fluctuations of iterated perturbed random walks in intermediate generations of a general branching process tree (with B. Rashytov and A. Iksanov), Lithuanian Mathematical Journal, 62, 447–466.

2021

  1. Sieving random iterative function systems (with I. Molchanov), Bernoulli, 27, no. 1, 34-65 (link to the official journal homepage).
  2. Moderate parts in regenerative compositions: the case of regular variation(with D. Buraczewski and B. Dovgay), Journal of Mathematical Analysis and Applications, 497, no. 1, 124894.
  3. A fundamental problem of hypothesis testing with finite inventory in e-commerce (with D. Bohle and M. Meiners), Applied Stochastic Models in Business and Industry, 37, 454-474.
  4. On the local time of a recurrent random walk on Z^2 (with V. Bohun), Theory of Probability and Mathematical Statistics, 105, 69-78.

2020

  1. Random walks in a strongly sparse random environment (with D. Buraczewski, P. Dyszewski, A. Iksanov), Stochastic Processes and their Applications, 130, no. 7, 3990-4027.
  2. Self-similar solutions of kinetic-type equations: the boundary case (with D. Buraczewski and K. Bogus), Stochastic Processes and their Applications, 130, no. 2, 677–693.
  3. The laws of iterated and triple logarithms for extreme values of regenerative processes (with I. Matsak), Modern Stochastics: Theory and Applications, 7, no. 1, 61-78.
  4. How long is the convex minorant of a one-dimensional random walk? (with G. Alsmeyer, Z. Kabluchko and V. Vysotsky), Electronic Journal of Probability, 25, paper no. 105.
  5. Stationary limits of renewal shot noise processes (with G. Verovkin), Theory of Probability and Mathematical Statistics, 101, 67-83. Ukrainian version.

2019

  1. Cones generated by random points on half-spheres and convex hulls of Poisson point processes (with Z. Kabluchko, D. Temesvari and C. Thäle), Probability Theory and Related Fields, 170, no. 3, 1021-1061.
  2. Limit theorems for the least common multiple of a random set of integers (with G. Alsmeyer and Z. Kabluchko), Transactions of the American Mathematical Society, 372, no. 7, 4585–4603.
  3. On the least common multiple of several random integers (with A. Bostan and K. Raschel), Journal of Number Theory, 204, 113-133.
  4. Random walks in a moderately sparse random environment (with D. Buraczewski, P. Dyszewski, A. Iksanov and A. Roitershtein), Electronic Journal of Probability, 24, paper no. 69.

2018

  1. On perpetuities with gamma-like tails (with D. Buraczewski, P. Dyszewski and A. Iksanov), Journal of Applied Probability, 55, no. 2, 368-389.
  2. The collision spectrum of Lambda-coalescents (with A.Gnedin, A. Iksanov and M. Moehle), Annals of Applied Probability, 28, no. 6, 3857-3883 (link to the official journal homepage).

2017

  1. A leader-election procedure using records (with G. Alsmeyer and Z. Kabluchko), Annals of Probability, 45, no, 6B, 4348-4388.
  2. Asymptotics of random processes with immigration I: scaling limits (with A. Iksanov and M. Meiners), Bernoulli, 23, no. 2, 1233-1278 (link to the official journal homepage).
  3. Asymptotics of random processes with immigration II: convergence to stationarity (with A. Iksanov and M. Meiners), Bernoulli, 23, no. 2, 1279-1298 (link to the official journal homepage).
  4. Fractionally integrated inverse stable subordinators (with A. Iksanov, Z. Kabluchko and G. Shevchenko), Stochastic Processes and their Applications, 127, no. 1, 80-106. 
  5. Functional limit theorems for the number of occupied boxes in the Bernoulli sieve (with G. Alsmeyer and A. Iksanov),  Stochastic Processes and their Applications, 127, no. 3, 995-1017.
  6. General Edgeworth expansions with applications to profiles of random trees (with Z. Kabluchko and H. Sulzbach), Annals of Applied Probability, 27, no. 6, 3478-3524. An extended preprint version (46 pages) is available here.
  7. A functional limit theorem for random processes with immigration in the case of heavy tails (with G. Verovkin), Modern Stochastics: Theory and Applications, 4, no. 2, 93-108.

2016

  1. Leader election using random walks (with G. Alsmeyer and Z. Kabluchko), ALEA – Latin American Journal of Probability and Statistics,  13, 1095-1122.
  2. Renewal approximation for the absorption time of a decreasing Markov chain (with G. Alsmeyer),  Journal of Applied Probability, 53(3), 765-782.
  3. Weak convergence of renewal shot noise processes in the case of slowly varying normalization (with A. Iksanov and Z. Kabluchko), Statistics and Probability Letters, 114, 67-77.
  4. Moment convergence of first-passage times in renewal theory (with A. Iksanov and M. Meiners),  Statistics and Probability Letters, 119, 134-143.
  5. Renewal shot noise processes in the case of slowly varying tails (with Z. Kabluchko),  Theory of Stochastic Processes, 21(37), 14-21.
  6. Local universality for real roots of random trigonometric polynomials (with A. Iksanov and Z. Kabluchko), Electronic Journal of Probability, no 68, 1-19.
  7. Mode and Edgeworth expansion for the Ewens distribution (with Z. Kabluchko and H. Sulzbach),

    Journal of Integer Sequences, 19, Article 16.8.8

2015

  1. Weak convergence of finite-dimensional distributions of the number of empty boxes in the Bernoulli sieve  (with A. Iksanov and V. Vatutin), Theory of Probability and its Applications, 59, 87-113 (this is an English translation of the item 2 in 2014 year).
  2. Optimal doubling strategies in backgammon (with S. Dotsenko), Contributions to Game Theory and Management, 8, 33–46.
  3. A note on convergence to stationarity of random processes with immigration, Theory of Stochastic Processes, 20(36), 84-100.

2014

  1. Weak convergence of the number of zero increments in the random walk with barrier (with G. Verovkin), Electronic Communications in Probability, 19, Article #74, 1-12.
  2. Finite-dimensional convergence of the number of empty boxes in the Bernoulli sieve (with A. Iksanov and V. Vatutin), Teor. Veroyatnost. i Primenen., 59, no. 1, 28-60.
  3. Limit theorems for renewal shot noise processes with eventually decreasing response functions (with A. Iksanov and M. Meiners), Stochastic Processes and their Applications, 124, no.6, 2132-2170. An extended preprint version (57 pages) is available here.
  4. On asymptotics of the beta-coalescents (with A. Gnedin, A. Iksanov and M. Moehle), Advances in Applied Probability, 46, no. 2, 496-515.
  5. Lambda-coalescents: a survey (with A. Gnedin and A. Iksanov), Journal of Applied Probability, Special Volume 51A, 23-40.
  6. Hint, extortion, and guessing games in the best choice problem (with S. Dotsenko), Cybernetics and Systems Analysis, 50, no. 3, 419-425.
  7. Birth defects on Chernobyl radionuclide polluted territories (with O. I. Timchenko, O.V. Linchak, O.V. Protsiuk, E.A. Pol’ka and Iu.V. Benedichuk), Radiatsionnaia Biologiia, Radioecologiia, 54, no. 5, 507-521.

2013

  1. Censorship game in optimal choice problem (with S. Dotsenko), Cybernetics and Systems Analysis, 49, no. 5, 749-755.

2012

  1. Exponential-uniform identities related to records (with A. Gnedin), Electronic Communications in Probability, 17, Article #26, 1-5.
  2. A Generalization of the Erdős–Turán Law for the Order of Random Permutation (with A. Gnedin and A. Iksanov), Combinatorics, Probability and Computing, 21, no. 5, 715-733.

2011

  1. Asymptotic behavior of moments of random recursive sequences (in Ukrainian), Reports of National Academy of Sciences of Ukraine, 3, 23-27.
  2. Lambda-coalescents with dust component (with A. Gnedin and A. Iksanov), Journal of Applied Probability, 48, no. 4, 1133-1151.

2010

  1. On the asymptotics of moments of linear random recurrences, Theory of Stochasctic Processes, 16(32), no. 2,106–119.
  2. Limit theorems for the number of occupied boxes in the Bernoulli sieve (with A.Gnedin and A. Iksanov), Theory of Stochastic Processes, 16(32), no.2, 44-57.
  3. Asymptotic behavior of absorption time of decreasing Markov chains, Bulletin of Taras Shevchenko National University of Kyiv, 1, 118-121.
  4. The Bernoulli sieve: an overview (with A.Gnedin and A. Iksanov), Discrete Mathematics and Theoretical Computer Science, Proceedings Series, AM, 329-342.

2009

  1. On the number of collisions in beta(2,b)-coalescents (with A. Iksanov and M. Moehle), Bernoulli, 15, no. 3, 829-845.

2008

  1. A note on non-regular martingales (with A. Iksanov), Statistics and Probability Letters, 78, 17, 3014–3017.
  2. Some applications of the Gnedenko-Korolyuk method to empirical distributions (with E. Lutsenko and I. Matsak), Theory of Probability and Mathematical Statistics, 78, 133-146.