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
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
2.
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
3.
A. A. Khartov, “Some criteria of rational-infinite divisibility for probability laws”, Electronic Journal of Probability, 30 (2025) , 29 pp.
4.
A. A. Khartov, “On decomposition problem for distribution functions of class $\boldsymbol{Q}$”, Proceedings of AMS, 2025, 1–15 (to appear)
5.
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
6.
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
7.
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
8.
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
9.
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
10.
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
11.
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
12.
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
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
A. A. Khartov, “On representation of the logarithm for arbitrary characteristic function on segments”, J. Math. Sci. (N. Y.), 286:5 (2024), 807–820
18.
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
19.
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. 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
21.
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
22.
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
23.
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
24.
M. Zani, A. A. Khartov, “On a decomposition of additive random fields”, Vestn. St. Petersbg. Univ., Math., 7:1 (2020), 29–36
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
29.
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
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
34.
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
35.
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
36.
A. A. Khartov, “Average approximation of tensor product-type random fields of increasing dimension”, J. Math. Sci. (N. Y.), 188:6 (2013), 769–782
37.
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
38.
I. S. Sineva, Khartov A.A., “Markovskie metody v postroenii profilya polzovatelya”, Trudy Moskovskogo Tekhnicheskogo Universiteta Svyazi i Informatiki, 2 (2008), 138–141
