01.01.05 (Probability theory and mathematical statistics)
Birth date:
30.12.1946
Keywords:
branching processes,
discrete probability problems,
probabilistic inequalities,
applications of discrete probability.
Subject:
Nesessary and sufficient conditions for almost sure extinction of bounded branching processes were established for discrete and for continuous time. Limit theorems were proved for:
a) $\varphi$–branching processes, b) critical decomposable branching processes with two types of particles and infinite second moments of offsprings,
c) distance to the nearest mutual ancestor of all simultaneously existing particles in a branching process,
d) conditional distributions of the number of particles on the life spans of branching process with immigration.
Limit distributions of a statistical estimate for the entropy of the polynomial distribution with growing number of outcomes were described. Explicit estimates of the rate of convergence of renewal density were found. Limit theorems and inequalities for distributions of random variables related with repeating tuples of outcomes in iid sequence were proved (in joint papers with V. G. Mihailov). Explicit inequalities for the accuracy of Poisson or compound Poisson approximations for the distributions of sums of functions of independent random variables were obtained. Explicit inequalities for taboo probabilities in Markov chains; these inequalities were used in the proofs of limit theorems for the time to the first occurence of rare event and for the frequencies of outcomes in a trajectories of discrete Markov chains with growing state space. A method to prove probabilistic inequalities by means of quadratic forms was elaborated and applied to the probabilities of the union of events, to the moments of ratios of positive random variables, to the generating functions and to the Laplace transforms.
Biography
Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 1970 (department of probability theory). Ph.D. thesis was defended in 1972. D.Sci. thesis was defended in 1982. A list of papers contains more than 40 titles.
A. M. Zubkov, A. V. Prokhorov, “Chair of Mathematical Statistics and Random Processes”, Moscow Univ. Math. Bull., 80:1 (2025), 34–41
2024
2.
Yu. S. Kharin, A. M. Zubkov, “On statistical testing of composite hypotheses on $s$-dimensional uniform probability distribution of binary sequences”, Diskr. Mat., 36:1 (2024), 116–135
2023
3.
A. M. Zubkov, A. A. Serov, “Experimental study of NIST Statistical Test Suite ability to detect long repetitions in binary sequences”, Matem. vopr. kriptogr., 14:2 (2023), 137–145
A. M. Zubkov, “Iteratsii sluchainykh otobrazhenii konechnykh mnozhestv”, Materialy II mezhdunarodnoi konferentsii “Teoreticheskaya i prikladnaya kriptografiya” (Minsk, 19–20 oktyabrya 2023g.), BGU, Minsk, 2023, 76–84
5.
A. M. Zubkov, “Statistical tests for uniformity of distribution and independence of vectors based on pairwise distances”, Matem. vopr. kriptogr., 14:3 (2023), 55–70
2022
6.
M. V. Filina, A. M. Zubkov, “Computation of distributions of the Kolmogorov-Smirnov statistic for finite samples”, Computer Data Analysis and Modeling: Stochastics and Data Science, Proceedings of the XIII International Conference (Minsk, Sepmember, 6–10, 2022), eds. Yu. Kharin et al., BSU, Minsk, 2022, 31–33
7.
A. M. Zubkov, A. A. Serov, “Notes on the independence of tests and on the completeness of NIST package”, Computer Data Analysis and Modeling: Stochastics and Data Science, Proceedings of the XIII International Conference (Minsk, Sepmember, 6–10, 2022), eds. Yu. Kharin et al., BSU, Minsk, 2022, 241–244
2024
8.
A. M. Zubkov, P. V. Khalipov, “Probability that given vertices belong to the same connected component of random equiprobable mapping”, Discrete Math. Appl., 34:4 (2024), 245–250
2021
9.
A. M. Zubkov, A. A. Serov, “A natural approach to the experimental study of dependence between statistical tests”, Matem. vopr. kriptogr., 12:1 (2021), 131–142
A. M. Zubkov, “Entropy as the quality characteristic of random sequences”, Mat. Vopr. Kriptogr., 12:3 (2021), 31–48
2020
11.
A. M. Zubkov, G. I. Ivchenko, Yu. I. Medvedev, “The roots of generating functions and sums of integer-valued random variables”, Mat. Vopr. Kriptogr., 11:1 (2020), 27–46
2022
12.
A. M. Zubkov, M. V. Filina, “Computation of distributions of statistics by means of Markov chains”, Discrete Math. Appl., 32:4 (2022), 285–295
2020
13.
A. M. Zubkov, “Estimates for the variational distance between two sets of independent random variables”, Mat. Vopr. Kriptogr., 11:3 (2020), 21–29
2019
14.
A. M. Zubkov, O. P. Orlov, “Almost-Linear Segments of Graphs of Functions”, Math. Notes, 106:5 (2019), 720–726
15.
A. M. Zubkov, A. A. Serov, “Testing the NIST Statistical Test Suite on artificial pseudorandom sequences”, Matem. vopr. kriptogr., 10:2 (2019), 89–96
Zubkov A. M., “Recent results on the total variation distance”, Computer Data Analysis and Modeling: Stochastics and Data Science, Proceedings of the XII International Conference (Minsk, September 18–22, 2019), Publishing Center of BSU, Minsk, 2019, 128–131
17.
Serov A. A., Zubkov A. M., “Testing the NIST Statistical Test Suite on artificial pseudorandom sequences”, Computer Data Analysis and Modeling: Stochastics and Data Science, Proceedings of the XII International Conference (Minsk, September 18–22, 2019), Publishing Center of BSU, Minsk, 2019, 291–294
18.
A. M. Zubkov, “Predelnye teoremy, svyazannye s algoritmami vybora sluchainykh elementov grupp”, Veroyatnostnye metody v diskretnoi matematike, X Mezhdunarodnaya Petrozavodskaya konferentsiya (22–26 maya, 2019 g., Petrozavodsk, Rossiya), KarNTs RAN, Petrozavodsk, 2019, 76–78
19.
A. M. Zubkov, A. A. Serov, “Moschnost obraza podmnozhestva pri kompozitsii sluchainykh otobrazhenii konechnogo mnozhestva”, Veroyatnostnye metody v diskretnoi matematike, X Mezhdunarodnaya Petrozavodskaya konferentsiya (22–26 maya, 2019 g., Petrozavodsk, Rossiya), KarNTs RAN, Petrozavodsk, 2019, 79–81
2018
20.
A. M. Zubkov, A. A. Serov, “Estimates of the mean size of the subset image under composition of random mappings”, Discrete Math. Appl., 28:5 (2018), 331–338
21.
A. M. Zubkov, V. I. Kruglov, “On quantiles of minimal codeword weights of random linear codes over $\mathbf{F}_p$”, Matem. vopr. kriptogr., 9:2 (2018), 99–102
A. M. Zubkov, “New estimates for the variational distance between two distributions of a sample”, Mat. Vopr. Kriptogr., 9:3 (2018), 45–60
23.
A. M. Zubkov, V. I. Kruglov, Review of Applied and Industrial Mathematics, 25:3 (2018), 249–251
24.
A. M. Zubkov, A. A. Serov, “Limit theorem for the size of an image of subset under compositions of random mappings”, Discrete Math. Appl., 28:2 (2018), 131–138
25.
A. M. Zubkov, O. P. Orlov, “Limit distributions of extremal distances to the nearest neighbor”, Discrete Math. Appl., 28:3 (2018), 189–199
2017
26.
Vasiliy Kruglov, Andrey Zubkov, “Number of Pairs of Template Matchings in $q$-ary Tree with Randomly Marked Vertices”, Analytical and Computational Methods in Probability Theory, Proceedings of the conference (Moscow, Russia, October 23–27, 2017), Lecture Notes in Comput. Sci., 10684, ACMPT 2017, eds. V. V. Rykov, N. D. Singpurwalla, A. M. Zubkov, Springer, 2017, 336–346
Marina Filina, Andrey Zubkov, “Algorithm of exact computation of decomposable statistics distributions and its applications”, Analytical and Computational Methods in Probability Theory, Proceedings of the conference (Moscow, Russia, October 23–27, 2017), Lecture Notes in Comput. Sci., 10684, eds. V. V. Rykov, N. D. Singpurwalla, A. M. Zubkov, Springer, 2017, 476–484
A. M. Zubkov, V. O. Mironkin, “Distribution of the length of aperiodicity segment in the graph of $k$-fold iteration of uniform random mapping”, Mat. Vopr. Kriptogr., 8:4 (2017), 63–74
2018
29.
A. M. Zubkov, K. A. Kolesnikova, “Limit theorem for the additive replacement process”, Theory Probab. Appl., 62:2 (2018), 319–327
2017
30.
A. M. Zubkov, M. P. Savelov, “Convergence of the sequence of the Pearson statistics values to the normalized square of the Bessel process”, Discrete Math. Appl., 27:6 (2017), 405–411
2016
31.
M. V. Filina, A. M. Zubkov, “Some remarks on the noncentral Pearson statistics distributions”, Computer Data Analysis and Modeling: Theoretical and Applied Stochastics, Proceedings of the XI International Conference (Minsk, September 6-10, 2016), eds. S. Aivazian, P. Filzmoser, Y. Kharin, Publishing center of BSU, Minsk, 2016, 155–158
32.
A. A. Serov, A. M. Zubkov, “Two-sided inequalities for the average number of elements in the union of images of finite set under iterations of random equiprobable mappings”, Computer Data Analysis and Modeling. Theoretical and Applied Stochastics, Proceedings of the XI International Conference (Minsk, September 6-10, 2016), Publishing Center of BSU, Minsk, 2016, 55–57
33.
A. M. Zubkov, V. I. Kruglov, “On coincidences of tuples in a binary tree with randomly labelled vertices”, Computer Data Analysis and Modeling. Theoretical and Applied Stochastics, Proceedings of the XI International Conference (Minsk, September 6-10, 2016), Publishing Center of BSU, Minsk, 2016, 189–192
34.
È. È. Gasanov, A. M. Zubkov, N. V. Klykova, “The algorithm for identical object searching with bounded worst-case complexity and linear memory”, Discrete Math. Appl., 26:5 (2016), 273–278
35.
Andrey M. Zubkov, Kseniya A. Kolesnikova, “A Markov chain with number-theoretic limit distribution”, Discrete Math. Appl., 26:2 (2016), 125–130
36.
A. M. Zubkov, V. I. Kruglov, “On coincidences of tuples in a binary tree with random labels of vertices”, Discrete Math. Appl., 26:3 (2016), 145–153
2015
37.
A. M. Zubkov, A. A. Serov, “Dvustoronnie neravenstva dlya srednikh chisel elementov v ob'edineniyakh obrazov konechnogo mnozhestva pri iteratsiyakh sluchainykh ravnoveroyatnykh otobrazhenii”, XVI Vserossiiskii Simpozium po prikladnoi i promyshlennoi matematike (osennyaya otkrytaya sessiya) (Sochi–Dagomys, 27 sentyabrya – 4 oktyabrya 2015 g.), Obzor. prikl. i prom. matem., 22, no. 5, 2015
2014
38.
A. M. Zubkov, V. I. Kruglov, “Statistical characteristics of weight spectra of random linear codes over $\mathrm{GF}(p)$”, Mat. Vopr. Kriptogr., 5:1 (2014), 27–38
39.
A. M. Zubkov, V. I. Kruglov, “Probabilistic characteristics of weight spectra of random linear subcodes over $\mathrm{GF}(p)$”, Prikl. Diskr. Mat. Suppl., 2014, no. 7, 118–121
40.
A. M. Zubkov, “Moments of weights of random nonuniform Boolean functions”, Mat. Vopr. Kriptogr., 5:3 (2014), 5–15
2015
41.
A. M. Zubkov, B. I. Selivanov, “On a statistic for testing the homogeneity of polynomial samples”, Discrete Math. Appl., 25:2 (2015), 109–120
42.
A. M. Zubkov, A. A. Serov, “Images of subset of finite set under iterations of random mappings”, Discrete Math. Appl., 25:3 (2015), 179–185
2014
43.
A. M. Zubkov, V. I. Kruglov, “On the vectors' weights in random linear spaces over $\mathrm{GF}(p)$”, Review of Applied and Industrial Mathematics, 21:4 (2014), 366–368
2013
44.
V. E. Tarakanov, A. M. Zubkov, “Cycle structure of power mappings in a residue classes ring”, Discrete Math. Appl., 23:3-4 (2013), 273–298
45.
A. M. Zubkov, T. A. Tatarenko, “The Equivalence between the Schur Order and the Stochastic Orders Generated by the Scheme of Allocation of Particles into Cells”, Math. Notes, 93:1 (2013), 69–74
46.
M. V. Filina, A. M. Zubkov, “Differences between the Pearson statistics distribution function and non-central chi-square distribution function”, Plenary lecture, Computer data analysis and modeling, Proceedings of the Tenth International conference (Minsk, September 10–14, 2013), v. 1, Publishing center of BSU, Minsk, 2013, 138–139
47.
A. M. Zubkov, V. I. Kruglov, “Weight spectra of random linear codes”, Computer data analysis and modeling, Proceedings of the Tenth International conference (Minsk, September 10–14, 2013), v. 2, Publishing center of BSU, Minsk, 2013, 20–22
48.
D. O. Menshenin, A. M. Zubkov, “Hypotheses testing for binary sequences obtained by the Neumann transform”, Computer data analysis and modeling, Proceedings of the Tenth International conference (Minsk, September 10–14, 2013), v. 2, Publishing center of BSU, Minsk, 2013, 23–25
49.
A. M. Zubkov, “New inequalities for the binomial law and for the total variation distance between iid samples”, Computer data analysis and modeling, Proceedings of the Tenth International conference (Minsk, September 10–14, 2013), v. 2, Publishing center of BSU, Minsk, 2013, 48–50
50.
A. M. Zubkov, N. P. Salikhov, “Inequalities of Probability Theory: A Collection. Chapter XI. Deviations of the distribution function of sums of independent variables from a specific distribution function”, Review of Applied and Industrial Mathematics, 20:4 (2013), 481–524
51.
A. M. Zubkov, N. P. Salikhov, “Inequalities of Probability Theory: A Collection. Chapter IX. Inequalities for distribution of maximum of sums of random variables”, Review of Applied and Industrial Mathematics, 20:2 (2013), 104–130
2012
52.
A. M. Zubkov, D. O. Men'shenin, “Properties of the Székely–Móri Symmetry Criterion Statistics in the Case of Binary Vectors”, Math. Notes, 91:4 (2012), 517–527
53.
A. M. Zubkov, M. V. Filina, “Exact computation of distributions by means of Markov chains”, Prikl. Diskr. Mat. Suppl., 2012, no. 5, 114–116
54.
A. M. Zubkov, A. A. Serov, “Estimates for the number of Boolean functions having affine or quadratic approximations with a given accuracy”, Prikl. Diskr. Mat. Suppl., 2012, no. 5, 11–13
55.
A. M. Zubkov, V. I. Kruglov, “On distributions of weight spectra for random linear binary codes”, Prikl. Diskr. Mat. Suppl., 2012, no. 5, 10–11
56.
A. M. Zubkov, A. A. Serov, “Nezamechennye nailuchshie neravenstva dlya binomialnogo zakona”, Mezhdunarodnaya konferentsiya «Teoriya veroyatnostei i eë prilozheniya», posvyaschënnaya 100-letiyu so dnya rozhdeniya B. V. Gnedenko (Moskva, 26–30 iyunya), Tezisy dokladov, LENAND, 2012, 35–36
57.
A. A. Serov, A. M. Zubkov, “Testing properties of Boolean mappings”, Workshop Current Trends in Cryptology (Nizhny Novgorod, 2 July), 2012, 32
58.
A. M. Zubkov, V. I. Kruglov, “Moments of codeword weights in random binary linear codes”, Mat. Vopr. Kriptogr., 3:4 (2012), 55–70
59.
A. Zubkov, V. Kruglov, “On the Distribution of Weight Spectra of Random Linear Binary Codes”, Proceedings of Workshop on Current Trends in Cryptology (Nizhny Novgorod), 2012, 29–31
60.
A. M. Zubkov, D. O. Menshenin, “Svoistva statistiki kriteriya simmetrichnosti Shekeli i Mori v sluchae dvoichnykh vektorov”, Mezhdunarodnaya konferentsiya «Teoriya veroyatnostei i eë prilozheniya», posvyaschënnaya 100-letiyu so dnya rozhdeniya B. V. Gnedenko (Moskva, 26–30 iyunya), Tezisy dokladov, LENAND, 2012, 35–34
61.
A. M. Zubkov, T. A. Tatarenko, “Ekvivalentnost ryada otnoshenii poryadka na mnozhestve diskretnykh raspredelenii”, Mezhdunarodnaya konferentsiya «Teoriya veroyatnostei i eë prilozheniya», posvyaschënnaya 100-letiyu so dnya rozhdeniya B. V. Gnedenko (Moskva, 26–30 iyunya), Tezisy dokladov, LENAND, 2012, 37–38
62.
A. M. Zubkov, M. V. Filina, “Svoistva raspredeleniya statistiki Pirsona dlya konechnykh vyborok”, Mezhdunarodnaya konferentsiya «Teoriya veroyatnostei i eë prilozheniya», posvyaschënnaya 100-letiyu so dnya rozhdeniya B. V. Gnedenko (Moskva, 26–30 iyunya), Tezisy dokladov, LENAND, 2012, 39–40
2013
63.
A. M. Zubkov, A. A. Serov, “A complete proof of universal inequalities for distribution function of binomial law”, Theory Probab. Appl., 57:3 (2013), 539–544
2012
64.
A. M. Zubkov, V. I. Kruglov, “On the distribution of weight spectra of random linear subspaces”, Review of Applied and Industrial Mathematics, 19:4 (2012), 564–566
65.
A. M. Zubkov, N. P. Salikhov, “Inequalities of Probability Theory: A Collection. Chapter V. Inequalities for joint distributions of two random variables”, Review of Applied and Industrial Mathematics, 19:4 (2012), 498–528
66.
A. M. Zubkov, N. P. Salikhov, “Inequalities of Probability Theory: A Collection. Chapter III. Inequalities for moments of functions in several variables”, Review of Applied and Industrial Mathematics, 19:2 (2012), 97–192
2011
67.
M. V. Filina, A. M. Zubkov, “Tail properties of Pearson statistics distributions”, Austrian J. Statistics, 40:1-2 (2011), 47–54
2012
68.
A. M. Zubkov, N. A. Kharitonova, E. V. Khil, “Gaps between local maxima in sequences of random variables”, Theory Probab. Appl., 56:4 (2012), 590–601
2011
69.
A. M. Zubkov, N. P. Salikhov, “Kollektsiya neravenstv teorii veroyatnostei. Glava I. Neravenstva dlya momentov funktsii ot sluchainoi velichiny”, Obozrenie prikl. i promyshl. matem., 18:6 (2011), 863–959
2010
70.
A. A. Serov, A. M. Zubkov, “On the number of Boolean functions in a given neighbourhood of the affine functions set”, Computer Data Analysis and Modeling: Complex Sthohastic Data and Systems, Proc. of the 9th Intern. Conf. (Minsk, 7–11 September 2010), v. 2, BSU, 2010, 67–70
71.
A. M. Zubkov, A. A. Serov, “Otsenki chisla bulevykh funktsii, imeyuschikh affinnye priblizheniya zadannoi tochnosti”, Materialy Kh Mezhdunarodnogo seminara «Diskretnaya matematika i ee prilozheniya» (Moskva, 1–6 fevralya 2010 g.), Izd-vo mekhaniko-matematicheskogo fakulteta MGU, 2010, 230–232
72.
A. M. Zubkov, A. A. Serov, “Bounds for the number of Boolean functions admitting affine approximations of a given accuracy”, Discrete Math. Appl., 20:5-6 (2010), 467–486
73.
A. M. Zubkov, “Computation of distributions of the numbers of components and cyclic points for random mappings”, Mat. Vopr. Kriptogr., 1:2 (2010), 5–18
74.
N. A. Kharitonova, E. V. Khil, A. M. Zubkov, “Goodness-of-fit test based on local maxima”, Proc. CDAM'2010, v. 1, Minsk, 2010, 74–76
2009
75.
A. M. Zubkov, A. A. Serov, “Srednee chislo podfunktsii sluchainoi bulevoi funktsii, blizkikh k mnozhestvu affinnykh funktsii”, X Vserossiiskii simpozium po prikladnoi i promyshlennoi matematike (osennyaya sessiya) (Sochi, 1–8 oktyabrya 2009 g.), Obozrenie prikl. i promyshl. matem., 16, no. 4, TVP, 2009, 657–658
76.
A. M. Zubkov, A. A. Serov, “Otsenki chisla bulevykh funktsii, imeyuschikh affinnye priblizheniya zadannoi tochnosti”, X Vserossiiskii simpozium po prikladnoi i promyshlennoi matematike (vesennyaya sessiya) (Sankt-Peterburg, 19–24 maya 2009 g.), Obozrenie prikl. i promyshl. matem., 16, no. 2, TVP, 2009, 337–339
77.
A. M. Zubkov, B. I. Selivanov, “Novaya statistika dlya proverki odnorodnosti polinomialnykh vyborok”, Obozrenie prikl. i promyshl. matem., 16:1 (2009)
78.
A. M. Zubkov, P. V. Khalipov, “Veroyatnost popadaniya neskolkikh tochek v odnu komponentu sluchainogo otobrazheniya”, Obozrenie prikl. i promyshl. matem., 16:2 (2009)
79.
A. M. Zubkov, N. A. Kharitonova, E. V. Khil, “Formuly dlya raspredelenii rasstoyanii mezhdu sosednimi lokalnymi maksimumami”, Obozrenie prikl. i promyshl. matem., 16:4 (2009)
80.
A. M. Zubkov, O. K. Shibanov, “Time Required to Unify All Particles in the Scheme of Equiprobable Allocation into a Sequence of Cell Layers”, Math. Notes, 85:3 (2009), 366–373
2008
81.
A. M. Zubkov, D. V. Sokolov, “Algoritmy chastichnoi sortirovki mnozhestv summ”, Matematicheskie voprosy kibernetiki, 17, eds. N. A. Karpova, Fizmatlit, M., 2008, 225–234
82.
M. V. Filina, A. M. Zubkov, “Exact computation of Pearson statistics distribution and some experimental results”, Austrian J. Statistics, 37:1 (2008), 129–135
A. M. Zubkov, D. O. Menshenin, “On the Szekely–Mori asymmetry criterion statistics for binary vectors with independent components”, Austrian J. Statistics, 37:1 (2008), 137–144
2011
84.
A. M. Zubkov, “Euler and combinatorial calculus”, Proc. Steklov Inst. Math., 274, suppl. 1 (2011), 162–168
2008
85.
A. M. Zubkov, “Probabilistic representations of some measures connected with factorizations”, Tr. Diskr. Mat., 11, no. 2, Fizmatlit, Moscow, 2008, 43–50
2007
86.
R. R. Gil'manshin, A. M. Zubkov, N. A. Kolokol'nikova, “Bounds for extremal values of the mean number of cells containing a given number of particles”, Discrete Math. Appl., 17:1 (2007), 7–12
2006
87.
A. M. Zubkov, O. K. Shibanov, “A Poisson limit theorem for a two-stage equiprobable scheme of allocating particles into cells”, Discrete Math. Appl., 16:6 (2006), 541–546
88.
M. V. Butakova, A. M. Zubkov, “Realizatsiya algoritma tochnogo vychisleniya raspredeleniya statistiki Pirsona v ravnoveroyatnoi polinomialnoi skheme”, Obozrenie prikl. i promyshl. matem., 13:6 (2006), 1022–1023
2005
89.
A. M. Zubkov, D. V. Shuvaev, “Calculation of moments of combinatorial statistics of symmetrically dependent random variables”, Discrete Math. Appl., 15:2 (2005), 109–123
90.
A. M. Zubkov, “Notes on statistical tests for nonidentically distributed observations”, Austrian J. Statistics, 34:2 (2005), 225–232
2003
91.
A. M. Zubkov, “Generators of pseudorandom numbers and their applications”, Moscow University and the development of cryptography in Russia, Inform. Bezop. Kriptografiya, MTsNMO, Moscow, 2003, 200–206
2002
92.
A. M. Zubkov, “Computational algorithms for distributions of sums of random variables”, Tr. Diskr. Mat., 5, Fizmatlit, Moscow, 2002, 51–60
2001
93.
A. M. Zubkov, “Estimates for maximal sizes of zero submatrices of a random $(0,1)$-matrix”, Tr. Diskr. Mat., 4, Fizmatlit, Moscow, 2001, 51–56
2000
94.
A. M. Zubkov, “Isomorphisms between sets of probability distributions”, Theory Probab. Appl., 44:4 (2000), 794–797
1998
95.
A. M. Zubkov, V. G. Mikhailov, “Estimation of the minimum number of outcomes with a given total probability”, Tr. Diskr. Mat., 2, TVP, Moscow, 1998, 101–111
1999
96.
A. M. Zubkov, “Two-sided inequalities for Laplace transforms”, Theory Probab. Appl., 43:4 (1999), 676–681
1997
97.
A. M. Zubkov, “Peculiarities of two-dimensional distributions of a sequence generated by a linear congruential generator”, Tr. Diskr. Mat., 1, TVP, Moscow, 1997, 113–120
1996
98.
A. M. Zubkov, “Neravenstva dlya momentov otnosheniya sluchainykh velichin”, Obozrenie prikl. i promyshl. matem., 3:4 (1996), 549–566
99.
A. M. Zubkov, “Rekurrentnye formuly dlya raspredelenii funktsionalov ot diskretnykh sluchainykh velichin”, Obozrenie prikl. i promyshl. matem., 3:4 (1996), 567–573
1994
100.
A. M. Zubkov, “Neravenstva dlya chisla odnovremenno proiskhodyaschikh sobytii”, Obozrenie prikl. i promyshl. matem., 1:4 (1994), 638–666
1993
101.
V. A. Vatutin, A. M. Zubkov, “Branching processes. II”, Probability theory and mathematical statistics, 1, J. Soviet Math., 67:6 (1993), 3407–3485
A. M. Zubkov, B. A. Sevastyanov, V. P. Chistyakov, Sbornik zadach po teorii veroyatnostei, 2-e izd., ispr. i dop., Nauka, M., 1989 , 320 pp.
1988
103.
A. M. Zubkov, “Estimates for sums of finitely dependent indicators and for the instant of first occurrence of a rare event”, Proc. Steklov Inst. Math., 177 (1988), 33–48
1987
104.
A. M. Zubkov, “On compound probabilistic metrics with given minimal metric”, Theory Probab. Appl., 31:1 (1987), 135–137
1985
105.
A. M. Zubkov, “On compound probabilistic metrics with given minimal metrics”, Stability problems for stochastic models (Uzhgorod, 1984), Lecture Notes in Math., 1155, Springer, Berlin, 1985, 443–447
1987
106.
V. A. Vatutin, A. M. Zubkov, “Branching processes. I”, J. Soviet Math., 39:1 (1987), 2431–2475
1983
107.
I. S. Badalbaev, A. M. Zubkov, “A limit theorem for a sequence of branching processes with nonhomogeneous immigration”, Dokl. Akad. Nauk UzSSR, 1983, no. 5, 3–4
1984
108.
I. S. Badalbaev, A. M. Zubkov, “Limit theorems for a sequence of branching processes with immigration”, Theory Probab. Appl., 28:2 (1984), 404–409
1982
109.
A. M. Zubkov, N. N. Popov, “Partial order relation generated by distributions of the number of occupied cells”, Math. Notes, 32:1 (1982), 528–531
1983
110.
A. M. Zubkov, “The limit behaviour of decomposable critical branching processes with two types of particles”, Theory Probab. Appl., 27:2 (1983), 235–237
1981
111.
A. M. Zubkov, “Examples of complex metrics for which minimal ones are zero ones”, Problems of stability of stochastic models (Panevezhis, 1980), Vsesoyuz. Nauch.-Issled. Inst. Sistem. Issled., Moscow, 1981, 39–41
112.
A. M. Zubkov, “Explicit estimates in the law of large numbers for sequences with mixing”, Sov. Math. Dokl., 24 (1981), 577–579
113.
A. M. Zubkov, Approksimatsii zavisimykh sluchainykh velichin nezavisimymi i ikh primeneniya, Diss. … dokt. fiz.-matem. nauk, MIAN, M., 1981
1980
114.
A. M. Zubkov, B. A. Sevastyanov, V. P. Chistyakov, Sbornik zadach po teorii veroyatnostei, Nauka, M., 1980 , 224 pp.
1979
115.
A. M. Zubkov, “Probabilistic proof of a geometric theorem”, Math. Notes, 26:6 (1979), 982–983
116.
A. M. Zubkov, “Markov chains close to a sequence of independent trials”, Math. Notes, 25:3 (1979), 243–248
1980
117.
A. M. Zubkov, “Inequalities for transition probabilities with taboos and their applications”, Math. USSR-Sb., 37:4 (1980), 451–488
1979
118.
A. M. Zubkov, V. G. Mihaǐlov, “On the repetitions of $s$-tuples in a sequence of independent trials”, Theory Probab. Appl., 24:2 (1979), 269–282
119.
A. M. Zubkov, V. G. Mihaǐlov, “On the accuracy of Poisson approximation in an occupancy problem”, Theory Probab. Appl., 23:4 (1979), 789–794
1977
120.
A. M. Zubkov, “Inequalities for the distribution of a sum of functions of independent random variables”, Math. Notes, 22:5 (1977), 906–914
1976
121.
A. M. Zubkov, “Dostatochnye usloviya skhodimosti posledovatelnosti sluchainykh potokov k ordinarnomu puassonovskomu potoku”, Trudy III Vsesoyuznogo soveschaniya po teorii massovogo obsluzhivaniya, v. 2, Izd-vo MGU, M., 1976, 197–202
1975
122.
A. M. Zubkov, “On the rate of convergence of a renewal density”, Math. USSR-Sb., 27:1 (1975), 131–142
1976
123.
A. M. Zubkov, “Limit distributions of distance to the nearest mutual ancestor”, Theory Probab. Appl., 20:3 (1976), 602–612
1975
124.
A. M. Zubkov, “Analogues between Galton–Watson processes and $\varphi$-branching processes”, Theory Probab. Appl., 19:2 (1975), 309–331
1974
125.
B. A. Sevast'yanov, A. M. Zubkov, “Controlled branching processes”, Theory Probab. Appl., 19:1 (1974), 14–24
126.
A. M. Zubkov, V. G. Mikhailov, “Limit distributions of random variables connected with long duplications in a sequence of independent trials”, Theory Probab. Appl., 19:1 (1974), 172–179
127.
A. M. Zubkov, “Limit distributions of a statistical estimate for the entropy”, Theory Probab. Appl., 18:3 (1974), 611–618
1973
128.
A. M. Zubkov, B. A. Sevastyanov, “Reguliruemye vetvyaschiesya protsessy”, Mezhdunar. konf. po teorii veroyatnostei i matematicheskoi statistike (Vilnyus, 1973), Tezisy dokladov, v. 2, Vilnyus, 1973, 223–224
129.
A. M. Zubkov, “A condition of degeneracy of a bounded branching process with continuous time”, Theory Probab. Appl., 17:2 (1973), 284–297
1972
130.
A. M. Zubkov, “Life-Periods of a Branching Process with Immigration”, Theory Probab. Appl., 17:1 (1972), 174–183
131.
A. M. Zubkov, Usloviya vyrozhdeniya modifitsirovannykh vetvyaschikhsya protsessov, Diss. … kand. fiz.-matem. nauk, MIAN, M., 1972
1970
132.
A. M. Zubkov, “A condition for the extinction of a bounded branching process”, Math. Notes, 8:1 (1970), 472–477
Presentations in Math-Net.Ru
1.
Отдел дискретной математики A. M. Zubkov Conference MIAN-90, dedicated to the 90th anniversary of Steklov Mathematical Institute May 15, 2024 16:30
Limit distributions of extreme distances to the nearest neighbor A. M. Zubkov, O. P. Orlov XV International Conference «Algebra, Number Theory and Discrete Geometry: modern problems and applications», dedicated to the centenary of the birth of the Doctor of Physical and Mathematical Sciences, Professor of the Moscow State University Korobov Nikolai Mikhailovich May 29, 2018 16:00
2025
