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), 1–17https://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), 1392–1409https://doi.org/10.3150/22-BEJ1503
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, “Criteria of relative and stochastic compactness for distributions of sums of independent random variables”, Theory Probab. Appl., 63:1 (2018), 57–71
6.
I. A. Alexeev, A. A. Khartov, “Spectral representations of characteristic functions of discrete probability laws”, Bernoulli, 29:2 (2023), 1392–1409https://doi.org/10.3150/22-BEJ1503
A. A. Khartov, “Average approximation of tensor product-type random fields of increasing dimension”, J. Math. Sci. (N. Y.), 188:6 (2013), 769–782
10.
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
11.
A. A. Khartov, “On representation of the logarithm for arbitrary characteristic function on segments”, J. Math. Sci. (N. Y.), 286:5 (2024), 807–820
12.
A. A. Kravchenko, A. A. Khartov, “Asymptotics of average case approximation complexity for tensor products of Euler integrated processes”, J. Math. Sci. (N. Y.), 281:1 (2024), 103–110
13.
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
14.
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
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
17.
A. A. Khartov, “Approksimatsiya mnogoparametricheskikh protsessov Andersona–Darlinga”, Zapiski nauchnykh seminarov POMI, 515, Veroyatnost i statistika. 33 (2022), 214-232http://ftp.pdmi.ras.ru/pub/publicat/znsl/v515/p214.pdf
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
21.
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
22.
A. A. Khartov, “Some criteria of rational-infinite divisibility for probability laws”, Electronic Journal of Probability, 30 (2025) , 29 pp.
23.
A. A. Khartov, “On decomposition problem for distribution functions of class $\boldsymbol{Q}$”, Proceedings of AMS, 2025, 1–15 (to appear)
24.
A. A. Khartov, On necessary conditions of rational-infinite divisibility for distributions with non-zero discrete parts, 2025 , 11 pp., arXiv: https://arxiv.org/abs/2509.07244
25.
A. A. Khartov, The class $\boldsymbol{Q}$ and mixture distributions with dominated continuous singular parts, 2025 , 34 pp., arXiv: https://arxiv.org/abs/2505.01148
26.
A. A. Khartov, Denseness in total variation and the class of rational-infinitely divisible distributions, 2025 , 18 pp., arXiv: https://arxiv.org/abs/2510.24219
27.
A. A. Khartov, “Rational-infinite divisibility of mixture probability laws with dominated continuous singular parts”, Computer Data Analysis and Modelling: Stochastics and Data Science. Proceedings of the XIV International Conference. (Minsk, 24–27 sentyabrya 2025 g.), BSU, 2025, 125–128https://conf.bsu.by/data/cdam_en/doc/CDAM
28.
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
29.
I. A. Alexeev, A. A. Khartov, “Density evolution for GLDPC codes”, 2024 IEEE International Multi-Conference on Engineering, Computer and Information Sciences (SIBIRCON) (Novosibirsk, 30 sentyabrya –2 oktyabrya 2024 g.), 2024, 80–84https://ieeexplore.ieee.org/document/10758497
30.
A. A. Khartov, “General criteria for belonging to the class of rational-infinitely divisible distributions”, XIV Belorusskaya matematicheskaya konferentsiya, posvyaschennaya 65-letiyu Instituta matematiki. Materialy mezhdunarodnoi nauchnoi konferentsii v 3-kh chastyakh (Minsk, 28 oktyabrya - 1 noyabrya 2024 g.), 2, Belaruskaya navuka, 2024, 161-162https://mmf.bsu.by/wp-content/uploads/2024/10/Tom-2.pdf
31.
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), 1–17https://doi.org/10.1214/23-EJP1032
32.
K. A. Tregubova, A. A. Khartov,, “Summy nezavisimykh sluchainykh velichin i obobschennye zakony Dikmana”, Zapiski nauchnykh seminarov POMI, 515, Veroyatnost i statistika. 33 (2022), 199-213http://ftp.pdmi.ras.ru/pub/publicat/znsl/v515/p199.pdf
33.
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, 296–298http://conf.uran.ru/kungurka/School-2012.pdf
34.
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
35.
I. S. Sineva, Khartov A.A., “Markovskie metody v postroenii profilya polzovatelya”, Trudy Moskovskogo Tekhnicheskogo Universiteta Svyazi i Informatiki, 2 (2008), 138–141
36.
K. A. Pyatkin, A. A. Khartov, “On approximation complexity in average case setting for tensor degrees of random processes”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 12:1 (2025), 76–90
37.
A. A. Khartov, I. S. Kharchenkov, “On some conditions for rationally-infinite divisibility of discrete distributions”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 12:2 (2025), 299–314
38.
M. Zani, A. A. Khartov, “On a decomposition of additive random fields”, Vestn. St. Petersbg. Univ., Math., 7:1 (2020), 29–36
