Publications

Books:

  1. Perpetuities, branching random walk and selfdecomposability (in Ukrainian), monograph, KTI-PRINT: Kiev, 2007, 192 p. Available upon request.
  2. “Renewal theory for perturbed random walks and similar processes“, Probability and its Applications, Birkhäuser, 2016.

Lecture notes:

  1. Statistics of shot noise processes with exponential response function, Kyiv University, 2002, 61 p.
  2. Non-negative infinitely divisible distributions, electronic version, 2003.
  3. Theory of characteristic functions (with V.I.Tyuptya and V.I. Shevchenko), Kyiv University, 2004, 46 p.
  4. Methods of transportation theory (with V.I. Shevchenko), Kyiv University, 2010, 85 p.
  5. Flows in networks (with V.I. Shevchenko), Kyiv University, 2010, 45 p.
  6. Discrete-time martingales, electronic version, 2011, 88 p.
  7. Elements of renewal theory, with applications, electronic English version, 2017, 112 p.
  8. Selected chapters in stochastic processes, electronic version in Ukrainian, 2013, 127 p.
  9. Lectures on generating functions, Laplace transforms and characteristic functions, electronic English version, 2021, 106 p.
    Slides for the 32 hours course of lectures given in Xidian university (Xi’an, China) on July 05-21, 2021:
    Generating functions
    Laplace transforms
    Characteristic functions

Submitted papers:

  1. “A law of the iterated logarithm for iterated random walks, with application to random recursive trees” (with Z. Kabluchko and V. Kotelnikova), submitted on October 10, 2023, 16 pages (preprint version).
  2. “On a discrete approximation of a skew stable Lévy process” (with C. Dong and A. Pilipenko), submitted on February 02, 2024, 23 pages (preprint version).
  3. “On decoupled standard random walks” (with G. Alsmeyer and Z. Kabluchko), submitted on February 08, 2024, 27 pages; revision submitted on August 23, 2024 (revised preprint version).
  4. “Laws of the iterated and single logarithm for sums of independent indicators, with applications to the Ginibre point process and Karlin’s occupancy scheme” (with D. Buraczewski and V. Kotelnikova), submitted on March 21, 2024, 46 pages (preprint version).
  5. “Convolution powers of unbounded measures on the positive half-line” (with D. Buraczewski and A. Marynych), submitted on April 07, 2024, 21 pages (preprint version).
  6. “A law of the iterated logarithm for the number of blocks in regenerative compositions generated by gamma-like subordinators” (with W. Jedidi), submitted on June 12, 2024, 15 pages (preprint version).
  7. “Multinomial random combinatorial structures and r-versions of Stirling, Eulerian and Lah numbers” (with Z. Kabluchko, A. Marynych, and V. Wachtel), submitted on August 12, 2024, 53 pages (preprint version).

Published papers since 2001:

2024

  1. “Precise tail behavior of some Dirichlet series” (with V. Wachtel), Journal of Theoretical Probability, 37, 2704-2737 (journal version (open access)).
  2. “A law of the iterated logarithm for small counts in Karlin’s occupancy scheme” (with V. Kotelnikova), Modern Stochastics: Theory and Applications, 11, no. 2, 217-245 (journal version).
  3. “Asymptotic fluctuations in supercritical Crump-Mode-Jagers processes” (with K. Kolesko and M. Meiners), Annals of Probability, 52, no. 4, 1538-1606 (revised preprint version, published version).
  4. “On multidimensional locally perturbed standard random walks” (with C. Dong and A. Pilipenko), Lithuanian Mathematical Journal, to appear (revised preprint version; journal version).

2023

  1. “Renewal theory for iterated perturbed random walks on a general branching process tree: early generations” (with B. Rashytov and I. Samoilenko), Journal of Applied Probability, 60, no. 1, 45-67 (revised preprint version; journal version).
  2. “Recurrence and transience of random difference equations in the critical case” (with G. Alsmeyer), Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, 59, no. 2, 606-620 (published version; link to the official journal homepage).
  3. “Limit theorems for discounted convergent perpetuities II” (with A. Marynych and A. Nikitin), Electronic Journal of Probability, 28, article no. 15, 1-22 (published version).
  4. “On a skew stable Lévy process” (with A. Pilipenko), Stochastic Processes and their Applications, 156, 44-68 (published (open access) version).
  5. “Functional limit theorems for random walks perturbed by positive alpha-stable jumps” (with A. Pilipenko and B. Povar), Bernoulli, 29, no. 2, 1638-1662 (published version; link to the official journal homepage).
  6. “A limit theorem for a nested infinite occupancy scheme in random environment” (with O. Braganets), Austrian Journal of Statistics, 52, 1-12 (published version).
  7. “Limit theorems for random Dirichlet series” (with D. Buraczewski, C. Dong and A. Marynych),  Stochastic Processes and their Applications, 165, 246-274 (revised preprint version, published version).
  8. “Critical branching processes in a sparse random environment (with D. Buraczewski,  C. Dong and A. Marynych), Modern Stochastics: Theory and Applications, 10, no. 4, 397-411 (journal version).

2022

  1. “A functional limit theorem for nested Karlin’s occupancy scheme generated by discrete Weibull-like distributions” (with Z. Kabluchko and V. Kotelnikova), Journal of Mathematical Analysis and Applications, 507, no.2, 125798 (revised preprint version; journal version).
  2. “Central limit theorem for the least common multiple of a uniformly sampled m-tuple of integers” (with D. Buraczewski and A. Marynych), Journal of Number Theory, 233, 301-336 (revised preprint version; journal version).
  3. “Late levels of nested occupancy scheme in random environment” (with B. Mallein), Stochastic Models, 38, no.1, 130-166 (preprint version; journal version).
  4. “Renewal theory for iterated perturbed random walks on a general branching process tree: intermediate generations” (with V. Bohun, A. Marynych and B. Rashytov), Journal of Applied Probability, 59, no. 2, 421-446 (revised preprint version; journal version).
  5. “On intermediate levels of nested occupancy scheme in random environment generated by stick-breaking II” (with A. Marynych and I. Samoilenko), Stochastics, 94, no. 7, 1077-1101 (revised preprint version; journal version).
  6. “Asymptotics of arithmetic functions of GCD and LCM of random integers in hyperbolic regions” (with A. Marynych and K. Raschel), Results in Mathematics, 77, no. 4, article 165, 22 p. (published version).
  7. “Stable fluctuations of iterated perturbed random walks in intermediate generations of a general branching process tree” (with A. Marynych and B. Rashytov), Lithuanian Mathematical Journal, 62, no. 4, 447-466 (published version).
  8. “Small counts in nested Karlin’s occupancy scheme generated by discrete Weibull-like distributions” (with V. Kotelnikova), Stochastic Processes and their Applications, 153, 283-320 (published (open access) version).

2021

  1. “On the derivative martingale in a branching random walk” (with D. Buraczewski and B. Mallein), Annals of Probability, 49, no. 3, 1164-1204 (published version; link to the official journal homepage).
  2. “A functional limit theorem without centering for general shot-noise processes” (with B. Rashytov), Ukrainian Mathematical Journal, 73, no. 2, 181-202 (published English version; link to the journal Ukrainian version).
  3. “Functional limit theorems for discounted exponential functional of random walk and discounted convergent perpetuity” (with O. Kondratenko), Statistics and Probability Letters, 176, 109148 (revised preprint version; journal version).
  4. “Limit theorems for discounted convergent perpetuities” (with A. Nikitin and I.Samoilenko), Electronic Journal of Probability, 26, article no. 131, 1-25 (published version).
  5. “Gaussian fluctuations and a law of the iterated logarithm for Nerman’s martingale in the supercritical general branching process” (with K. Kolesko and M. Meiners), Electronic Journal of Probability, 26, paper no. 160, 1-22 (published version).

2020

  1. “Weak convergence of random processes with immigration at random times” (with C. Dong), Journal of Applied Probability, 57, no. 1, 250-265 (revised preprint version; journal version).
  2. “A functional limit theorem for general shot noise processes” (with B. Rashytov), Journal of Applied Probability, 57, no. 1, 280-294 (revised preprint version; journal version).
  3. “On nested infinite occupancy scheme in random environment” (with A. Gnedin), Probability Theory and Related Fields, 177, no. 3-4, 855-890 (published (open access) version).
  4. “Fluctuations of Biggins’ martingales at complex parameters” (with K. Kolesko and M. Meiners), Annales de l’Institut Henri Poincaré, Probabilites et Statistiques, 56, no. 4, 2445-2479 (published version; link to the official journal homepage).
  5. “Random walks in a strongly sparse random environment” (with D. Buraczewski, P. Dyszewski and A. Marynych), Stochastic Processes and their Applications, 130, no. 7, 3990-4027 (revised preprint version; journal version).
  6. “On intermediate levels of nested occupancy scheme in random environment generated by stick-breaking I” (with D. Buraczewski and B. Dovgay), Electronic Journal of Probability, 25, paper no. 123, 1-24 (published version).

2019

  1. “A result on power moments of Lévy-type perpetuities and its application to the Lp-convergence of Biggins’ martingales in branching Lévy processes” (with B. Mallein), ALEA Latin American Journal of Probability and Mathematical Statistics, 16, 315-331 (published version).
  2. “Random walks in a moderately sparse random environment” (with D. Buraczewski, P. Dyszewski, A. Marynych and A. Roitershtein), Electronic Journal of Probability, 24, paper no. 69, 1-44 (published version).
  3. “Stable-like fluctuations of Biggins’ martingales” (with K. Kolesko and M. Meiners), Stochastic Processes and their Applications, 129, no. 11, 4480-4499 (preprint version; published version).
  4. “On Lp-convergence of the Biggins martingale with complex parameter” (with Q. Liu and X. Liang), Journal of Mathematical Analysis and Applications, 479, 1653-1669 (preprint version; published version).

2018

  1. “Functional limit theorems for the number of busy servers in a G/G/\infty queue” (with W. Jedidi and F. Bouzeffour), Journal of Applied Probability, 55, no. 1, 15-29 (preprint version; journal version).
  2. “On perpetuities with gamma-like tails” (with D. Buraczewski, P. Dyszewski and A. Marynych), Journal of Applied Probability, 55, no. 2, 386-389 (preprint version; journal version).
  3. “Functional limit theorems for Galton-Watson processes with very active immigration” (with Z. Kabluchko), Stochastic Processes and their Applications, 128, no. 1, 291-305 (published version).
  4. “The collision spectrum of Lambda-coalescents” (with A. Gnedin, A. Marynych and M. Moehle), Annals of Applied Probability, 28, no. 6, 3857-3883 (published version; link to the official journal homepage).
  5. “A functional limit theorem for the profile of random recursive trees” (with Z. Kabluchko), Electronic Communications in Probability, 23, paper no. 87, 1-13 (published version).
  6. “Weak convergence of the number of vertices at intermediate levels of random recursive trees” (with Z. Kabluchko), Journal of Applied Probability, 55, no. 4, 1131-1142 (preprint version; journal version).

2017

  1. “Fractionally integrated inverse stable subordinators” (with Z. Kabluchko, A. Marynych and G. Shevchenko), Stochastic Processes and their Applications, 127, no. 1, 80-106 (published version).
  2. “Asymptotics of random processes with immigration I: scaling limits” (with A. Marynych and M. Meiners), Bernoulli, 23, no. 2, 1233-1278 (published version).
  3. “Asymptotics of random processes with immigration II: convergence to stationarity” (with A. Marynych and M. Meiners), Bernoulli, 23, no. 2, 1279-1298 (published version).
  4. “Functional limit theorems for the number of occupied boxes in the Bernoulli sieve” (with G. Alsmeyer and A. Marynych), Stochastic Processes and their Applications, 127, no. 3, 995-1017 (published version).
  5. “Functional limit theorems for the maxima of perturbed random walks and divergent perpetuities in the M1-topology” (with A. Pilipenko and I. Samoilenko), Extremes, 20, no. 3, 567-583 (preprint version; journal version).
  6. “A law of the iterated logarithm for the number of occupied boxes in the Bernoulli sieve” (with W. Jedidi and F. Bouzeffour), Statistics and Probability Letters, 126, 244-252 (preprint version; journal version).
  7. “Null recurrence and transience of random difference equations in the contractive case” (with G. Alsmeyer and D. Buraczewski), Journal of Applied Probability, 54, no. 4, 1089-1110 (preprint version; journal version).

2016

  1. “Weak convergence of renewal shot noise processes in the case of slowly varying normalization” (with Z. Kabluchko and A. Marynych), Statistics and Probability Letters, 114, 67-77 (preprint version; journal version).
  2. “Moment convergence of first-passage times in renewal theory” (with A. Marynych and M. Meiners), Statistics and Probability Letters, 119, 134-143 (preprint version; journal version).
  3. “Local universality for real roots of random trigonometric polynomials” (with Z. Kabluchko and A. Marynych), Electronic Journal of Probability, 21, paper no. 63, 19 pp. (published version).
  4. “Tail behavior of suprema of perturbed random walks” (with S. Polotskiy), Theory of Stochastic Processes, 21(36), no.1, 12-16 (published version).
  5. “A functional limit theorem for locally perturbed random walks” (with A. Pilipenko), Probability and Mathematical Statistics, 36, no. 2, 353-368 (published version).
  6. “A central limit theorem and a law of the iterated logarithm for the Biggins martingale of the supercritical branching random walk” (with Z. Kabluchko), Journal of Applied Probability, 53, no.4, 1178-1192 (preprint version; journal version).

2015

  1. “Rate of convergence in the law of large numbers for supercritical general multi-type branching processes” (with M. Meiners), Stochastic Processes and their Applications, 125, no. 2, 708-738 (published version).
  2. “Functional limit theorems for divergent perpetuities in the contractive case” (with D. Buraczewski), Electronic Communications in Probability, 20, article 10, 1-14 (published version).
  3. “Power and exponential moments of the number of visits and related quantities for perturbed random walks” (with G. Alsmeyer and M. Meiners), Journal of Theoretical Probability, 28, no. 1, 1-40 (published version).
  4. “Weak convergence of finite-dimensional distributions of the number of empty boxes in the Bernoulli sieve” (with A. Marynych and V. Vatutin), Theory of Probability and its Applications, 59, 87-113 (preprint version; journal version).
  5. “Fixed points of multivariate smoothing transforms with scalar weights” (with M. Meiners), ALEA Latin American Journal of Probability and Mathematical Statistics, 12,69-114 (published version).
  6. “A two-type Bellman-Harris process initiated by a large number of particles” (with V. Vatutin and V. Topchii), Acta Applicandae Mathematicae, 138, 279-312 (published version).
  7. “Exponential moments of first passages times and related quantities for Lévy processes” (with F. Aurzada and M. Meiners), Mathematische Nachrichten, 288, 1921-1938 (preprint version; journal version).

2014

  1. “Limit theorems for renewal shot noise processes with eventually decreasing response functions” (with A. Marynych and M. Meiners), Stochastic Processes and their Applications, 124, no.6, 2132-2170 (extended preprint version 58 pages, journal version 43 pages).
  2. “On asymptotics of the beta-coalescents” (with A. Gnedin, A. Marynych and M. Moehle), Advances in Applied Probability, 46, no. 2, 496-515 (preprint version; journal version).
  3. “On the maximum of a perturbed random walk” (with A. Pilipenko), Statistics and Probability Letters, 92, 168-172 (preprint version; published version).
  4. “Lambda-coalescents: a survey” (with A. Gnedin and A. Marynych), Journal of Applied Probability, Special Volume 51A, 23-40 (published version).

2013

  1. “On the number of empty boxes in the Bernoulli sieve I”, Stochastics, 85, no.6, 946-959 (preprint version; journal version).
  2. “Functional limit theorems for renewal shot noise processes with increasing response functions”, Stochastic Processes and their Applications, 123, no.6, 1987-2010 (published version).

2012

  1. “Regenerative compositions in the case of slow variation: A renewal theory approach” (with A. Gnedin), Electronic Journal of Probability, 17, article 77, 1-19 (published version).
  2. “On the number of empty boxes in the Bernoulli sieve II”, Stochastic Processes and their Applications, 122, no.7, 2701-2729 (published version).
  3. “A generalization of the Erdös-Turán law for the order of random permutation” (with A. Gnedin and A. Marynych), Combinatorics, Probability and Computing, 21, no.5, 715-733 (preprint version; journal version).

2011

  1. “Lambda-coalescents with dust component” (with A. Gnedin and A. Marynych), Journal of Applied Probability, 48, no. 4, 1133-1151 (published version).
  2. “Moments of random sums and Robbins’ problem of optimal stopping” (with A. Gnedin), Journal of Applied Probability, 48, no. 4, 1197-1199 (published version).

2010

  1. “Exponential rate of almost sure convergence of intrinsic martingales in supercritical branching random walks” (with M. Meiners), Journal of Applied Probability, 47, no. 2, 513-525 (published version).
  2. “The Bernoulli sieve: an overview” (with A. Gnedin and A. Marynych), Discrete Mathematics and Theoretical Computer Science, Proceedings Series, Volume AM, 329-342 (published version).
  3. “Exponential moments of first passage times and related quantities for random walks” (with M. Meiners), Electronic Communications in Probability, 15, article 34, 365-375 (published version).
  4. “Limit theorems for the number of occupied boxes in the Bernoulli sieve” (with A. Gnedin and A. Marynych), Theory of Stochastic Processes, 16(32), no.2, 44-57 (published version).

2009

  1. “A limiting distribution for the number of cuts needed to isolate the root of a random recursive tree” (with M. Drmota, M. Moehle and U. Roesler), Random structures and algorithms, 34, no. 3, 319-336 (preprint version; journal version).
  2. “A log-type moment result for perpetuities and its application to martingales in supercritical branching random walks” (with G. Alsmeyer), Electronic Journal of Probability, 14, 289-313 (published version).
  3. “On distributional properties of perpetuities” (with G. Alsmeyer and U. Roesler), Journal of Theoretical Probability, 22, no. 3, 666-682 (journal version).
  4. “The Bernoulli sieve revisited” (with A. Gnedin, P. Negadajlov and U. Roesler), Annals of Applied Probability, 19, no. 4, 1634-1655 (published version).
  5. “On the number of collisions in beta (2,b)-coalescents” (with A. Marynych and M. Moehle), Bernoulli, 15, no. 3, 829-845 (published version).
  6. “Exponential rate of Lp-convergence of intrinsic martingales in supercritical branching random walks” (with G. Alsmeyer, S. Polotskiy and U.Roesler), Theory of Stochastic Processes, 15(31), no. 2, 1-18 (published version).

2008

  1. “On asymptotics of exchangeable coalescents with multiple collisions” (with A. Gnedin and M. Moehle), Journal of Applied Probability, 45, no. 4, 1186-1195 (published version).
  2. “On asymptotic behavior of certain recursions with random indices of linear growth” (with Yu. Terletsky), ProbStatForum, 1, 62-67 (published version).
  3. “A note on non-regular martingales” (with A. Marynych), Statistics and Probability Letters, 78, no.17, 3014-3017 (journal version).
  4. “On the number of jumps of random walks with a barrier” (with M. Moehle), Advances in Applied Probability, 40, no.1, 206-228 (published version).
  5. “On the number of zero increments of random walks with a barrier” (with P. Negadailov), Discrete Mathematics and Theoretical Computer Science, Proceedings Series Volume AI, 247-254 (published version).
  6. “Small parts in the Bernoulli sieve” (with A. Gnedin and U. Roesler), Discrete Mathematics and Theoretical Computer Science, Proceedings Series Volume AI, 239-246 (published version).

2007

  1. “A probabilistic proof of a weak limit law for the number of cuts needed to isolate the root of a random recursive tree” (with M.Moehle), Electronic Communications in Probability, 12, 28-35 (published version).
  2. “On the supremum of perturbed random walk”, Bulletin of Kiev University, n.1, 161-164.
  3. “Asymptotic results about the total branch length of the Bolthausen-Sznitman coalescent” (with M. Drmota, M. Moehle and U. Roesler), Stochastic Processes and their Applications, 117, no. 10, 1404-1421 (published version).
  4. “On an integro-functional equation related to fixed points of the smoothing transforms”, Bulletin of Kiev University, no.2, 151-154.

2006

  1. “On the rate of convergence of a regular martingale related to a branching random walk”, Ukrainian Mathematical Journal, 58, no. 3, 326-342 (journal version).
  2. “Some moment results about the limit of a martingale related to the supercritical branching random walk and perpetuities” (with U. Rösler), Ukrainian Mathematical Journal, 58, no. 4, 451-471 (published version).
  3. “On the supremum of a martingale related to the branching random walk” (with P. Negadajlov), T.Imov. ta Mat.Statist., 74, pp. 44-51.
  4. “On some moments of the limit random variable for a normalized supercritical Galton-Watson process”, In Focus on Probability Theory, L.R. Velle (ed.), Nova Science Publishers, Inc. (New-York), pp. 151-158.
  5. “Regular variation in the branching random walk” (with S. Polotskiy), Theory of Stochastic Processes, 12(28), no. 1-2, 38-54 (published version).
  6. “The Hurwitz zeta distribution” (with C.Y. Hu, G.D. Lin, O.K. Zakusylo), Australian and New Zealand Journal of Statistics, 48, no. 1, 1-6 (journal version).

2004

  1. “On a Pitman-Yor problem” (with C.S. Kim), Statistics and Probability Letters, 68, no.1, 61-72 (preprint version; journal version).
  2. “On a new factorization property of the selfdecomposable probability distributions on Banach spaces” (with Z.J. Jurek and B.M. Schreiber), Annals of Probability, 32, no. 2, 1356-1369 (published version).
  3. “New explicit examples of fixed points of Poisson shot noise transforms” (joinly with Che-Soong Kim), Australian and New Zealand Journal of Statistics, 46, no. 2, 313-321 (journal version).
  4. ” Elementary fixed points of the BRW smoothing transforms with infinite number of summands”, Stochastic Processes and their Applications, 114, no. 1, 27-50 (published version).
  5. “Infinite divisibility of infinite sums of lower records, a simple proof”, Journal of Applied Probability, 41, no. 4, 1187-1190.
  6. “A conjecture on the behavior of tails of fixed points of the shot noise transform”, Theory of Probability and Mathematical Statistics, 69, 55-60 (published version).

2003

  1. “Shot noise distributions and selfdecomposability” (with Z.J. Jurek), Stochastic Analysis and Applications, 21, no. 3, 593-609 (preprint version; journal version).

2002

  1. “Remarks concerning proofs of some results on selfdecomposability in Banach space”, Bulletin of Kiev University, ser. phys.-math.sciences, no.2, 221-227.
  2. “On fixed points of Poisson shot noise transforms” (with Z.J.Jurek), Advances in Applied Probability, 34, no. 4, 798-825 (preprint version; journal version).
  3. “On perpetuities related to the size-biased distributions”, Theory of Stochastic Processes, 8(24), no. 1-2, 128-135.
  4. “On positive distributions of the class L of self-decomposable laws”, Theor.Probability and Math.Statist. (translated by AMS from the Ukrainian journal), 64, 51-61 .

2001

  1. “Parameter estimation for the radioactive contamination process”, Studia Scientarum Mathematicarum Hungarica, 37, no.3-4, 237-258.