Denis Denisov

Probability and Statistics seminar

You can find information about upcoming seminars at Probability and Statistics seminars

Research interests

Probability Theory, Random Walks, Markov Chains.

PhD students

I am constantly looking for good candidates. Please do not to hesitate to contact me about possibility of a PhD in Probability.

Teaching

• Brownian motion. Year 2024-25, Semester 2.
• Stochastic Control. Year 2024-25, Semester 2.

Publications

[53]

D. Denisov, A. Tarasov, and Wachtel V. “Asymptotic expansions for normal deviations of random walks conditioned to stay positive ”. Submitted (2024). arXiv: TBA

[52]

D. Denisov, A. Tarasov, and Wachtel V. “Berry-Esseen inequality for random walks conditioned to stay positive ”. Submitted (2024). arXiv: 2412.08502 .

[51]

D. Denisov, W. FitzGerald and Wachtel V. “Ordered random walks and the Airy line ensemble ”. Submitted (2024). arXiv: 2411.17827 .

[50]

W.Cygan, D. Denisov, Z. Palmowski, and Wachtel V. “Stable random walks in cones”. Submitted (2024). arXiv: 2409.18200.

[49]

D. Denisov, A. Tarasov, and Wachtel V. “Expansions for random walks conditioned to stay positive”. Submitted (2024). arXiv: 2401.09929.

[48]

D. Denisov and K. Zhang “Markov chains in the domain of attraction of Brownian motion in cones”. J. Theoretical Probab. 38, article number 14, (2025). arXiv: 2309.16311 .

[47]

D. Denisov, N. Gotthardt, D. Korshunov, V. Wachtel “Probabilistic approach to risk processes with level-dependent premium rate”. Insurance: Mathematics and Economics 118, 142--156 (2024). arXiv: 2311.02484, DOI: https://doi.org/10.1016/j.insmatheco.2024.06.002.

[46]

D. Denisov and V. Wachtel. “Harmonic measure in a multidimensional gambler’s problem”. Ann. Appl. Probab. 34(5), 4387--4407 (2024). arXiv: 2212.11526 DOI: https://doi.org/10.1214/24-AAP2069.

[45]

D.Denisov and V. Wachtel. “Random walks in cones revisited”. Ann. Inst. H. Poincare(B) Probab. Statist. 60, 126 -- 166, (2024). arXiv: 2112.10244, DOI: https://doi.org/10.1214/22-AIHP1331.

[44]

D.Denisov and V. Wachtel. “Green function for an asymptotically stable random walk in a half space”. J. Theoretical Probab. 37(2), 1745--1786 (2024). arXiv: 2209.12603. DOI: https://doi.org/10.1007/s10959-023-01283-4. .

[43]

D.Denisov and W. FitzGerald. “Ordered exponential random walks”. ALEA, Lat. Am. J. Probab. Math. Stat. (2023), (20), pp. 1211–1246, arXiv: 2205.02556. DOI: https://doi.org/10.30757/ALEA.v20-45. .

[42]

D.Denisov, G. Hinchrich, M. Kolb and V. Wachtel. “Persistence of autoregressive sequences with logarithmic tails”. Elec. J. Probab. (2022), 27, pp. 1-43. arXiv: 2203.14772, DOI: https://doi.org/10.1214/22-EJP879.

[41]

D.Denisov, G. Hinchrich, A. Sakhanenko and V. Wachtel. “Crossing an Asymptotically Square-Root Boundary by the Brownian Motion”. Proceedings of the Steklov Institute of Mathematics , (2022), 316, 105 - 120. DOI: https://doi.org/10.1134/S0081543822010096.

[40]

D.Denisov and N. Walton. “Regret Analysis of a Markov Policy Gradient Algorithm for Multi-arm Bandits”. Math. Oper. Research (2022), 48, 1553–1588. arXiv: 2007.10229 DOI: https://doi.org/10.1287/moor.2022.1311.

[39]

D.Denisov, A. Sakhanenko and V. Wachtel. “First-passage times for random walks in the triangular array setting”. A Lifetime of Excursions Through Random Walks and Lévy Processes. Progr. Probab., Birkhauser, (2021), pp. 1–15. arXiv: 2005.00240 DOI: https://doi.org/10.1007/978-3-030-83309-1_10.

[38]

D.Denisov, E. Perfilev and V. Wachtel. “Tail asymptotics for the area under the excursion of a random walk with heavy-tailed increments”. J. Appl. Probab. (2021), 58(1), 217 - 237. arXiv: 1907.01280 DOI: https://doi.org/10.1017/jpr.2020.85.

[37]

D.Denisov, D. Korshunov and V. Wachtel. “Renewal Theory for Transient Markov Chains with Asymptotically Zero Drift”. Trans. Amer. Math. Soc. 373 , (2020), 7253-7286. arXiv: 1907.07940 DOI: https://doi.org/10.1090/tran/8167.

[36]

D.Denisov. “Maximum on a random time interval of a random walk with infinite mean”. Queueing Systems (2020), pp. 1–10. arXiv: arXiv:1907.08920 DOI: https://doi.org/10.1007/s11134-020-09661-z.

[35]

D.Denisov and V. Wachtel. “Alternative constructions of a harmonic function for a random walk in a cone”. Elec. J. Probab. (2019), pp. 1–26. arXiv: 1805.01437. DOI: 10.1214/19-EJP349.

[34]

D. Denisov, D. Korshunov, and V. Wachtel. “Markov chains on Z+: analysis of stationary measure via harmonic functions approach”. Queueing Systems 91(3-4) (2019), pp. 265–295. arXiv: 1312.2201. DOI: https://doi.org/10.1007/s11134-019-09602-5.

[33]

D. Denisov, A. Sakhanenko, and V. Wachtel. “ First-passage times over moving boundaries for asymptotically stable walks”. Theory Probab. Appl., (2019), 63(4), 613–633. arXiv: 1801.04136. DOI: https://doi.org/10.1137/S0040585X97T989283.

[32]

D. Denisov, A. Sakhanenko, and V. Wachtel. “First-passage times for random walks with non-identically distributed increments”. Ann. Probab. 46(6) (2018), 3313-3350.doi: 10.1214/17-AOP1248. arXiv: 1611.00493.

[31]

D. E. Denisov and N. N. Leonenko. “Multifractal scenarios for products of geometric Levy-based stationary models”. Stochastic Analysis and Applications 34.4 (2016), pp. 610–643. doi: 10.1080/07362994.2016.1164606.

[30]

D. Denisov, Korshunov D., and V. Wachtel. “At the Edge of Criticality: Markov Chains with Asymptotically Zero Drift”. Submitted (2016), pp. 1–213. arXiv: 1612.01592.

[29]

D. Denisov and N. Leonenko. “Limit theorems for multifractal products of geometric stationary processes”. Bernoulli 22.4 (2016), pp. 2579–2608. doi: 10.3150/15-BEJ738.

[28]

D. Denisov and V. Wachtel. “Exact asymptotics for the instant of crossing a curve boundary by an asymptotically stable random walk”. Probab. Theory Appl. 60.3 (2016), pp. 481–500. doi: 10.1137/S0040585X97T987740. arXiv: 1403.5918.

[27]

D. Denisov and V. Wachtel. “Universality of local times of killed and reflected random walks”. Electron. Commun. Probab. 21 (2016), 11 pp. doi: 10.1214/15-ECP3995.

[26]

D. Denisov, M. Kolb, and V. Wachtel. “Local asymptotics for the area of random walk excursions”. Journal of the London Mathematical Society 91.2 (2015), pp. 495–513. doi: 10.1112/jlms/jdu078.

[25]

D. Denisov and V. Wachtel. “Exit times for integrated random walks”. Ann. Inst. H. Poincare Probab. Statist. 51.1 (2015), pp. 167–193. doi: 10.1214/13-AIHP577. arXiv: 1207.2270.

[24]

D. Denisov and V. Wachtel. “Random walks in cones”. Ann. Probab. 43.3 (2015), pp. 992–1044. doi: 10.1214/13-AOP867. arXiv: 1110.1254.

[23]

D. Denisov and J. Kugler. “Heavy traffic and heavy tails for subexponential distributions”. Submitted (2014), pp. 1–26. arXiv: 1403.7325.

[22]

D. Denisov, V. Vatutin, and V. Wachtel. “Local probabilities for random walks with negative drift conditioned to stay nonnegative”. Electron. J. Probab. 19 (2014), pp. 1–17. doi: 10.1214/EJP.v19-3426.

[21]

D. Denisov, D. Korshunov, and V. Wachtel. “Potential analysis for positive recurrent Markov chains with asymptotically zero drift: Power-type asymptotics”. Stochastic Processes and their Applications 123.8 (2013), pp. 3027–3051. doi: 10.1016/j.spa.2013.04.011. arXiv: 1208.3066.

[20]

D. Denisov, D. Korshunov, and V. Wachtel. “Tail asymptotics for the supercritical Galton-Watson process in the heavy-tailed case”. Proceedings of the Steklov Institute of Mathematics 282.1 (2013), pp. 273–297. doi: 10.1134/S0081543813060205. arXiv: 1303.2306.

[19]

D. Denisov and V. Shneer. “Asymptotics for the first passage times of Levy processes and random walks”. J. Appl. Probab. 50.1 (2013), pp. 64–84. doi: 10.1239/jap/1363784425. arXiv: 0712.0728.

[18]

D. Denisov, S. Foss, and T. Konstantopoulos. “Limit theorems for a random directed slab graph”. Ann. Appl. Probab. 22.2 (2012), pp. 702–733. doi: 10.1214/11-AAP783. arXiv: 1005.4806.

[17]

D. Denisov and V. Wachtel. “Martingale approach to subexponential asymptotics for random walks”. Electron. Commun. Probab. 17 (2012), pp. 1–9. doi: 10.1214/ECP.v17-1757. arXiv: 1111.6810.

[16]

D. Denisov and V. Wachtel. “Ordered random walks with heavy tails”. Electron. J. Probab. 17 (2012), pp. 1–21. doi: 10.1214/EJP.v17-1719. arXiv: 1103.4529.

[15]

O. Boxma and D. Denisov. “Sojourn time tails in the single server queue with heavy-tailed service times”. Queueing Systems 69.2 (2011), pp. 101–119. doi: 10.1007/s11134-011-9229-y.

[14]

D. Denisov, S. Foss, and D. Korshunov. “Asymptotics of randomly stopped sums in the presence of heavy tails”. Bernoulli 16.4 (2010), pp. 971–994. doi: 10.3150/10-BEJ251. arXiv: 0808.3697.

[13]

D. Denisov and S. Shneer. “Global and local asymptotics for the busy period of an M/G/1 queue”. Queueing Systems 64.4 (2010), pp. 383–393. doi: 10.1007/s11134-010-9167-0.

[12]

D. Denisov and V. Wachtel. “Conditional Limit Theorems for Ordered Random Walks”. Electron. J. Probab. 15 (2010), pp. 292–322. doi: 10.1214/EJP.v15-752. arXiv: 0907.2854.

[11]

D. Denisov, T. Dieker, and V. Shneer. “Large deviations for random walks under subexponentiality: the big-jump domain”. Ann. Probab. 36.5 (2008), pp. 1946–1991. doi: 10.1214/07-AOP382. arXiv: math/0703265.

[10]

D. Denisov, S. Foss, and D. Korshunov. “Lower limits for distributions of randomly stopped sums”. Probab. Theory Appl. 52.4 (2008), pp. 1031–1046. doi: 10.1137/S0040585X97983328. arXiv: 0711.4491.

[9]

D. Denisov, S. Foss, and D. Korshunov. “On lower limits and equivalences for distribution tails of randomly stopped sums”. Bernoulli 14.2 (2008), pp. 391–404. doi: 10.3150/07-BEJ111. arXiv: math/0701920.

[8]

D. Denisov and V. Shneer. “Local asymptotics of the cycle maximum of a heavy-tailed random walk”. Adv. in Appl. Probab. 39.1 (2007), pp. 221–244. doi: 10.1239/aap/1175266476.

[7]

D. Denisov and B. Zwart. “On a theorem of Breiman and a class of random difference equations”. J. Appl. Probab. 44.4 (2007), pp. 1031–1046. doi: 10.1239/jap/1197908822.

[6]

D. Denisov and A. Sapozhnikov. “On the distribution of the number of customers in the symmetric M/G/1 queue”. Queueing Systems 54.4 (2006), pp. 237–241. doi: 10.1007/s11134-006-0298-2.

[5]

D.E. Denisov. “On the Existence of a Regularly Varying Majorant of an Integrable Monotone Function”. English. Mathematical Notes 79.1-2 (2006), pp. 129–133. doi: 10.1007/s11006-006-0013-y.

[4]

D. Denisov. “A note on the asymptotics for the maximum on a random time interval of a random walk”. Markov Processes and related fields 11 (2005), pp. 165–169.

[3]

D. Denisov, S. Foss, and D. Korshunov. “Tail Asymptotics for the Supremum of a Random Walk when the Mean Is not Finite”. Queueing Systems 46.1-2 (2004), pp. 15–33. doi: 10.1023/B:QUES.0000021140.87161.9c. arXiv: 1303.4715.

[2]

D. Denisov and S. Foss. “On Transience Conditions for Markov Chains and Random Walks”. Siberian Mathematical Journal 44.1 (2003), pp. 44–57. doi: 10.1023/A:1022008203109.

[1]

S. Foss and D. Denisov. “On Transience Conditions for Markov Chains”. Siberian Mathematical Journal 42.2 (2001), pp. 364–371. doi: 10.1023/A:1004801516561.

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