01.01.05 (Probability theory and mathematical statistics)
E-mail:
UDC:
519.21
Subject:
Characteristic functions and generalized Levy-Khinchine formulas.
Convergence, relative and stochastic compactness of sequences of distributions.
Infinitely divisible and rationally (quasi-)infinitely divisible distributions.
Decompositions of probability laws.
Approximation of random processes and fields.
Main publications:
I. A. Alexeev, A. A. Khartov, “A criterion and a Cramér-Wold device for quasi-infinite divisibility for discrete multivariate probability laws”, Electronic Journal of Probability, 28 (2023), 1–17 https://doi.org/10.1214/23-EJP1032
I. A. Alexeev, A. A. Khartov, “Spectral representations of characteristic functions of discrete probability laws”, Bernoulli, 29:2 (2023), 1392–1409 https://doi.org/10.3150/22-BEJ1503
A. A. Khartov, “On weak convergence of quasi-infinitely divisible laws”, Pacific Journal of Mathematics, 322:2 (2023), 341–367 (Published online) https://doi.org/10.2140/pjm.2023.322.341, arXiv: https://arxiv.org/abs/2204.13667
A. A. Khartov, “A criterion of quasi-infinite divisibility for discrete laws”, Statistics & Probability Letters, 185 (2022), 109436 https://www.sciencedirect.com/science/article/pii/S0167715222000426?via
A. A. Khartov, “Criteria of relative and stochastic compactness for distributions of sums of independent random variables”, Theory Probab. Appl., 63:1 (2018), 57–71
A. A. Khartov, “Asymptotic analysis of average case approximation complexity of Hilbert space valued random elements”, J. Complexity, 31:6 (2015), 835-866 http://www.sciencedirect.com/science/article/pii/S0885064X1500062X, arXiv: https://arxiv.org/abs/1410.4320
A. A. Khartov, I. A. Limar, “Asymptotic analysis in multivariate worst case approximation with Gaussian kernels”, Journal of Complexity, 2024 (to appear) , arXiv: https://arxiv.org/abs/2306.14239
2023
2.
I. A. Alexeev, A. A. Khartov, “Spectral representations of characteristic functions of discrete probability laws”, Bernoulli, 29:2 (2023), 1392–1409 https://doi.org/10.3150/22-BEJ1503
I. A. Alexeev, A. A. Khartov, “A criterion and a Cramér-Wold device for quasi-infinite divisibility for discrete multivariate probability laws”, Electronic Journal of Probability, 28 (2023), 1–17 https://doi.org/10.1214/23-EJP1032
5.
A. A. Khartov, Some criteria of rational infinite divisibility for distribution functions, 2023 , 17 pp., arXiv: 2305.14524
2022
6.
A. A. Khartov, I. A. Limar, “Asymptotic analysis in multivariate average case approximation with Gaussian kernels”, Journal of Complexity, 70 (2022), 101631 https://www.sciencedirect.com/science/article/pii/S0885064X21000868
A. A. Khartov, “A criterion of quasi-infinite divisibility for discrete laws”, Statistics & Probability Letters, 185 (2022), 109436 https://www.sciencedirect.com/science/article/pii/S0167715222000426?via
A. A. Khartov, “O predstavlenii logarifma proizvolnoi kharakteristicheskoi funktsii na otrezkakh”, Zapiski nauchnykh seminarov POMI, 510, Veroyatnost i statistika. 32 (2022), 262-281 http://ftp.pdmi.ras.ru/pub/publicat/znsl/v510/p262.pdf
9.
K. A. Tregubova, A. A. Khartov,, “Summy nezavisimykh sluchainykh velichin i obobschennye zakony Dikmana”, Zapiski nauchnykh seminarov POMI, 515, Veroyatnost i statistika. 33 (2022), 199-213 http://ftp.pdmi.ras.ru/pub/publicat/znsl/v515/p199.pdf
10.
A. A. Khartov, “Approksimatsiya mnogoparametricheskikh protsessov Andersona–Darlinga”, Zapiski nauchnykh seminarov POMI, 515, Veroyatnost i statistika. 33 (2022), 214-232 http://ftp.pdmi.ras.ru/pub/publicat/znsl/v515/p214.pdf
2021
11.
A. A. Kravchenko, A. A. Khartov, “Asymptotics of average case approximation complexity for tensor products of Euler integrated processes”, Probability and statistics. Part 31, Zap. Nauchn. Sem. POMI, 505, POMI, St. Petersburg, 2021, 147–161
12.
A. A. Kravchenko, A. A. Khartov, “An estimate of average case approximation complexity for tensor degrees of random processes”, Vestn. St. Petersbg. Univ., Math., 8:4 (2021), 351–360
13.
I. A. Alekseev, A. A. Khartov, “On convergence and compactness in variation with shift of discrete probability laws”, Vestn. St. Petersbg. Univ., Math., 8:4 (2021), 221–226
2020
14.
M. Zani, A. A. Khartov, “Ob odnom razlozhenii additivnykh sluchainykh polei”, Vestnik Sankt-Peterburgskogo Universiteta. Matematika. Mekhanika. Astronomiya, 7 (65):1 (2020), 39-49 http://vestnik.spbu.ru/html20/s01/s01v1/04.pdf
15.
A. A. Khartov, I. A. Alexeev, “Quasi-infinite divisibility and three-pointprobability laws”, Probability and statistics. Part 29, Zap. Nauchn. Sem. POMI, 495, POMI, St. Petersburg, 2020, 305–316
16.
M. Zani, A. A. Khartov, “On a decomposition of additive random fields”, Vestn. St. Petersbg. Univ., Math., 7:1 (2020), 29–36
2019
17.
A. A. Khartov, M. Zani, “Asymptotic analysis of average case approximation complexity of additive random fields”, Journal of Complexity, 52 (2019), 24–44 https://www.sciencedirect.com/science/article/abs/pii/S0885064X18300268
A. A.Khartov, M. Zani, “Approximation complexity of sums of random processes”, Journal of Complexity, 54 (2019), 101399 , 11 pp. https://www.sciencedirect.com/science/article/abs/pii/S0885064X19300214
A. A. Khartov, “Compactness criteria for quasi-infinitely divisible distributions on the integers”, Stat.&Prob. Letters, 153 (2019), 1–6 https://www.sciencedirect.com/science/article/abs/pii/S0167715219301373
A. A. Khartov, “Criteria of relative and stochastic compactness for distributions of sums of independent random variables”, Theory Probab. Appl., 63:1 (2018), 57–71
2017
21.
A. A. Khartov, “Stochastic compactness of distributions of sums of independent random variables with finite variances”, Lithuanian Mathematical Journal, 57:2 (2017), 196–203
A. A. Khartov, “A simplified criterion for quasi-polynomial tractability of approximation of random elements and its applications”, J. Complexity, 34 (2016), 30-41 (Published online) http://www.sciencedirect.com/science/article/pii/S0885064X15001247, arXiv: https://arxiv.org/abs/1503.02600
A. A. Khartov, “Characteristic functions and compactness for distributions of sums of independent random variables”, J. Math. Sci. (N. Y.), 229:6 (2018), 792–802
2015
24.
A. A. Khartov, “Asymptotic analysis of average case approximation complexity of Hilbert space valued random elements”, J. Complexity, 31:6 (2015), 835-866 http://www.sciencedirect.com/science/article/pii/S0885064X1500062X, arXiv: https://arxiv.org/abs/1410.4320
A. A. Khartov, “Approximation in probability of tensor product-type random fields of increasing parametric dimension”, J. Math. Sci. (N. Y.), 204:1 (2015), 165–179
2013
26.
A. A. Khartov, “Approximation complexity of tensor product-type random fields with heavy spectrum”, Vestnik of the St. Petersburg University: Mathematics, 46:2 (2013), 98-101
2012
27.
A. A. Khartov, “Approksimatsiya v srednem tenzornykh sluchainykh polei vozrastayuschei razmernosti”, Tezisy Mezhdunarodnoi (43-Vserossiiskoi) molodëzhnoi shkoly-konferentsii “Sovremennye problemy matematiki” (Ekaterinburg 29 yanv. – 5 fev. 2012), UroRAN Institut matematiki i mekhaniki, 2012, 296–298 http://conf.uran.ru/kungurka/School-2012.pdf
2013
28.
A. A. Khartov, “Average approximation of tensor product-type random fields of increasing dimension”, J. Math. Sci. (N. Y.), 188:6 (2013), 769–782
2008
29.
I. S. Sineva, Khartov A.A., “Matematicheskoe modelirovanie i analiz informatsionnykh potokov v web Usage Mining”, Trudy Moskovskogo Tekhnicheskogo Universiteta Svyazi i Informatiki, 2 (2008), 133–137
30.
I. S. Sineva, Khartov A.A., “Markovskie metody v postroenii profilya polzovatelya”, Trudy Moskovskogo Tekhnicheskogo Universiteta Svyazi i Informatiki, 2 (2008), 138–141
2024
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