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, “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, “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, “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, “Criteria of relative and stochastic compactness for distributions of sums of independent random variables”, Theory Probab. Appl., 63:1 (2018), 57–71
5.
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
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. 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
9.
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
10.
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, “Approximation complexity of tensor product-type random fields with heavy spectrum”, Vestnik of the St. Petersburg University: Mathematics, 46:2 (2013), 98-101
12.
A. A. Khartov, “Average approximation of tensor product-type random fields of increasing dimension”, J. Math. Sci. (N. Y.), 188:6 (2013), 769–782
13.
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. 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
15.
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, “Stochastic compactness of distributions of sums of independent random variables with finite variances”, Lithuanian Mathematical Journal, 57:2 (2017), 196–203
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
18.
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
19.
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
20.
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
21.
A. A. Khartov, Some criteria of rational infinite divisibility for distribution functions, 2023 , 17 pp., arXiv: 2305.14524
22.
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
23.
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
24.
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
25.
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
26.
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
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
28.
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
29.
I. S. Sineva, Khartov A.A., “Markovskie metody v postroenii profilya polzovatelya”, Trudy Moskovskogo Tekhnicheskogo Universiteta Svyazi i Informatiki, 2 (2008), 138–141
30.
M. Zani, A. A. Khartov, “On a decomposition of additive random fields”, Vestn. St. Petersbg. Univ., Math., 7:1 (2020), 29–36