Publications

  • M.S. thesis "Transition phenomena for Markov chains and their applications"
  • PhD thesis "Transition phenomena for real-valued Markov chains"
  • DSc thesis "Large deviation probabilities for asymptotically space homogeneous stable Markov chains"
  1. Transient phenomena for Markov chains and their applications, Adv. Appl. Probab. 24 (1992) 322-342 (with A. A. Borovkov and G. Fayolle). PDF file is available.
  2. Transient phenomena for real-valued Markov chains, Theory Probab. Appl. 38 (1993) 149-152. PDF file is available. The original publication is available at epubs.siam.org, PDF
  3. Transition phenomena for real-valued Markov chains, Siberian Advances in Mathematics 3(4) (1993) 53-100. PS file is available.
  4. Ergodicity in a sense of weak convergence, equilibrium-type identities and large deviations for Markov chains. Grigelionis, B. (ed.) et al., Probability theory and mathematical statistics. Proceedings of the sixth Vilnius conference. Utrecht: VSP (1994) 89-98 (with A. A. Borovkov). PDF file is available.
  5. Large deviation probabilities for one-dimensional Markov chains. I: Stationary distributions, Theory Probab. Appl. 41 (1996) 1-24 (with A. A. Borovkov). PDF file is available. The original publication is available at epubs.siam.org, PDF
  6. Tightness and continuity of a family of invariant measures for Markov chains depending on a parameter, Sib. Math. J. 37 (1996) 730-746. PS file is available. The original publication is available at www.springerlink.com, PDF
  7. On distribution tail of the maximum of a random walk, Stochastic Processes and Their Applications 72 (1997) 97-103. PDF file is available. The original publication is available at www.sciencedirect.com, PDF.
  8. Ergodicity of a polling network with an infinite number of stations, Queueing Systems 32 (1999) 169-193 (With A. A. Borovkov and R. Schassberger). PDF file is available. The original publication is available at www.springerlink.com, PDF.
  9. Large-deviation probabilities for one-dimensional Markov chains. Part 2. Prestationary distributions in the exponential case, Probability Theory and Its Applications 45 (2001) 379-405 (with A. A. Borovkov). PDF file is available. The original publication is available at epubs.siam.org, PDF
  10. Sampling at a random time with a heavy-tailed distribution, Markov Processes and Related Fields 6 (2000) 543-568 (with S. Foss). PDF file is available.
  11. Limit theorems for general Markov chains. Sib. Math. J. 42 (2001) 301-316. PDF file is available. The original publication is available at www.springerlink.com, PDF
  12. Large-deviation probabilities for maxima of sums of independent random variables with negative mean and subexponential distribution, Probability Theory and Its Applications 46 (2002) 355-366. PDF file is available. The original publication is available at epubs.siam.org, PDF
  13. Large-deviation probabilities for one-dimensional Markov chains. Part 3. Prestationary distributions in the subexponential case, Probability Theory and Its Applications 46 (2002) 603-618 (with A. A. Borovkov). PDF file is available. The original publication is available at epubs.siam.org, PDF
  14. Asymptotics for sums of random variables with local subexponential behaviour, Journal of Theoretical Probability 16 (2003) 489-518 (with S. Asmussen and S. Foss). PDF file is available. The original publication is available at www.springerlink.com, PDF
  15. Asymptotics for random walks with dependent heavy-tailed increments, Sib. Math. J. 44 (2003) 833-844 (with S. Schlegel and V. Schmidt). PDF file is available The original publication is available at www.springerlink.com, PDF
  16. One-dimensional asymptotically homogeneous Markov chains: Cram'er transform and large deviation probabilities, Siberian Advances in Mathematics 14(4), (2004) 30-70. PDF file is available.
  17. Tail asymptotics for the supremum of a random walk when the mean is not finite, Queueing Systems 46 (2004) 15-33 (with S. Foss and D. Denisov). PDF file is available. The original publication is available at www.springerlink.com, PDF.
  18. The critical case of the Cramer-Lundberg theorem on the asymptotic tail behavior of the maximum of a negative drift random walk, Siberian Mathematical Journal 46 (2005) 1077-1081. PDF file is available. The original publication is available at www.springerlink.com, PDF.
  19. Heavy tails in multi-server queue, Queueing Systems 52 (2006) 31-48 (with S. Foss). PDF file is available. The original publication is available at www.springerlink.com, PDF.
  20. On the distribution density of the supremum of a random walk in the subexponential case, Siberian Mathematical Journal 47 (2006) 1060-1065. PDF file is available. The original publication is available at www.springerlink.com, PDF.
  21. Lower limits and equivalences for convolution tails, The Annals of Probability 35 (2007) 366-383 (with S. Foss). PDF file is available. The original publication is available at projecteuclid.org, PDF
  22. Lower limits for distribution tails of randomly stopped sums, Theory Probab. Appl. 52 (2007) 690-699 (with D. Denisov and S. Foss). PDF file is available. The original publication is available at epubs.siam.org, PDF
  23. The key renewal theorem for a transient Markov chain, Journal of Theoretical Probability 21 (2008) 234–245. PDF file is available. The original publication is available at www.springerlink.com, PDF
  24. On lower limits and equivalences for distribution tails of randomly stopped sums, Bernoulli 14 (2008) 391–404 (with D. Denisov and S. Foss). PDF file is available. The original publication is available at projecteuclid.org, PDF
  25. Convolutions of long-tailed and subexponential distributions, Journal of Applied Probability 46 (2009) 756-767 (with S. Foss and S. Zachary). PDF file is available. The original publication is available at projecteuclid.org, PDF
  26. An analog of Wald's identity for random walks with infinite mean, Siberian Mathematical Journal 50 (2009) 663-666. PDF file is available. The original publication is available at www.springerlink.com, PDF
  27. Asymptotics of randomly stopped sums in the presence of heavy tails, Bernoulli 16 (2010) 971–994 (with D. Denisov and S. Foss). PDF file is available. The original publication is available at projecteuclid.org, PDF
  28. Local asymptotics for the time of first return to the origin of transient random walk, Statistics & Probability Letters 81 (2011) 1419–1424 (with R. A. Doney). PDF file is available. The original publication is available at ScienceDirect.com, PDF
  29. Moments for stationary Markov chains with asymptotically zero drift, Siberian Mathematical Journal 52 (2011) 655-664. PDF file is available. The original publication is available at www.springerlink.com, PDF
  30. How to measure the accuracy of the subexponential approximation for the stationary single server queue, Queueing Systems 68 (2011) 261–266. PDF file is available. The original publication is available at www.springerlink.com, PDF
  31. On large delays in multi-server queues with heavy tails, Mathematics of Operations Research, 37 (2012) 201–218 (with S. Foss). PDF file is available. The original publication is available at INFORMS website, PDF
  32. Potential analysis for positive recurrent Markov chains with asymptotically zero drift: Power-type asymptotics, Stochastic Processes and their Applications, 123 (2013) 3027--3051 (with D. Denisov and V. Wachtel). PDF file is available. The original publication is available at ScienceDirect website, PDF
  33. Tail asymptotics for the supercritical Galton-Watson process in the heavy-tailed case, Proceedings of the Steklov Institute of Mathematics, 282 (2013) 273–297 (with V. Wachtel and D. Denisov). PDF file is available. The original publication is available at www.springerlink.com, PDF
  34. On extremal behavior of Gaussian chaos, Doklady Mathematics, 88 (2013) 566–568 (with V. I. Piterbarg and E. Hashorva). PDF file is available. The original publication is available at www.springerlink.com, PDF
  35. Asymptotic expansion of Gaussian chaos via probabilistic approach, Extremes, 18 (2015) 315-347 (with V. I. Piterbarg and E. Hashorva). PDF file is available. The original publication is available at www.springerlink.com, PDF
  36. On the asymptotic Laplace method and its application to random chaos, Mathematical Notes, 97 (2015) 60–73 (with V. I. Piterbarg and E. Hashorva). PDF file is available. The original publication is available at www.springerlink.com, PDF
  37. Two-dimensional ruin probability for subexponential claim size, Probability and Mathematical Statistics, 37 (2017) 319-335 (with S. Foss, Z. Palmowski and T. Rolski). PDF file is available. The original publication is available at University of Wroclaw website, PDF
  38. On subexponential tails for the maxima of negatively driven compound renewal and L\'evy processes, Stochastic Processes and Their Applications, 128 (2018) 1316-1332. PDF file is available. The original publication is available at ScienceDirect website, PDF
  39. Markov chains on Z+: analysis of stationary measure via harmonic functions approach, Queueing Systems, 91 (2019) 265-295 (with D. Denisov and W. Wachtel). The original publication is available at ScienceDirect website, PDF
  40. Tail asymptotics for Shepp-statistics of Brownian motion in Rd, Extremes, 23 (2020) 35-54 (with W. Wang). The original publication is available at ScienceDirect website, PDF
  41. Strong law of large numbers for a function of the local times of a transient random walk in Zd, Journal of Theoretical Probability, (2019) - (with I. Asymont). The original publication is available at ScienceDirect website, PDF
  42. Renewal theory for transient Markov chains with asymptotically zero drift, Trans. Amer. Math. Soc., 373 (2020) 7253-7286 (with D. Denisov and W. Wachtel). The original publication is available at American Mathematical Society website, PDF

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