01.01.05 (Probability theory and mathematical statistics)
Birth date:
20.02.1941
E-mail:
Keywords:
limit theorems; Markovian and branching random processes; random permutations; statistical control of quality; statistical problems of discrete mathematics.
Subject:
The rate of convergence in multivariate central limit theorem is investigated for homogeneous Markovian chain with arbitrary set of states. Limit theorems on asymptotical behaviours of branching random processes with state-dependent immigration are proved. Properties of distributions of numerical characteristics of random permutations are established and asymptotic normality sets for these distributions are found. Explicit formulas for optimal plans of continuous sampling control are obtained and asymptotics of optimal sample volumes are indicated. The modified variant of Stein–Tikhomirov method is developed. With the help of this method non-classical limit theorems for sums of independent triangular arrays of random variables are proved.
Biography
Graduated from Faculty of Mathematics and Mechanics of Tashkent State University (TSU) in 1963 (department of probability theory and mathematical statistics). Ph.D. thesis was defended in 1968. D.Sci. thesis was defended in 1976. A list of my works contains more than 150 titles. I lead the scientific seminar in Institute of Mathematics of Uzbek Academy of Sciences on probability theory and mathematical statistics.
Academician of Uzbek Academy of Sciences. In 1975 I was awarded the State prize of Uzbekistan after Beruni for a series of investigations on limit theorems of probability theory (jointly with S. Kh. Sirajdinov and T. A. Azlarov).
Main publications:
Formanov Sh. K., Mirvaliev M. Grneralized chi-square Statistics for embedded samples // MMR'2000. Second International Conference on Mathematical Methods in Reliability. Methodology, Practise and Inference, v. 1, p. 405–409.
Sh. K. Formanov, “Another proof of a Sakhanenko theorem”, Teor. Veroyatnost. i Primenen., 67:3 (2022), 591–596; Theory Probab. Appl., 67:3 (2022), 473–477
I. A. Ibragimov, E. L. Presman, Sh. K. Formanov, “On modifications of the Lindeberg and Rotar' conditions in the central limit theorem”, Teor. Veroyatnost. i Primenen., 65:4 (2020), 818–822; Theory Probab. Appl., 65:4 (2021), 648–651
Sh. K. Formanov, A. N. Startsev, S. S. Sedov, “Limit theorems for the generalized size of epidemic in a Markov model with immunization”, Diskr. Mat., 25:4 (2013), 103–115; Discrete Math. Appl., 24:2 (2014), 73–82
Sh. K. Formanov, “On the Stein–Tikhomirov method and its applications in nonclassical limit theorems”, Diskr. Mat., 19:1 (2007), 27–39; Discrete Math. Appl., 17:1 (2007), 23–36
Sh. K. Formanov, “The Stein–Tikhomirov Method and a Nonclassical Central Limit Theorem”, Mat. Zametki, 71:4 (2002), 604–610; Math. Notes, 71:4 (2002), 550–555
S. H. Siraždinov, š. K. Formanov, “On the estimates of the rate of convergence in the central limit theorem for homogeneous Markov chains”, Teor. Veroyatnost. i Primenen., 28:2 (1983), 219–228; Theory Probab. Appl., 28:2 (1984), 229–239
S. Kh. Sirazhdinov, Sh. K. Formanov, M. M. El-Fahham, “On estimates of the remainder term in a local theorem for the densities of sums of independent random variables”, Dokl. Akad. Nauk SSSR, 232:3 (1977), 532–534
1975
8.
Sh. K. Formanov, “On invariance principles for homogeneous Markov chains”, Dokl. Akad. Nauk SSSR, 221:1 (1975), 42–44
1972
9.
Sh. K. Formanov, “On rate of convergence in the multidimensional central limit theorem for homogeneous Markov chains”, Dokl. Akad. Nauk SSSR, 204:1 (1972), 49–51
1970
10.
M. Mamatov, Sh. K. Formanov, “Estimating probabilities for sums of independent random vectors”, Mat. Zametki, 7:2 (1970), 217–221; Math. Notes, 7:2 (1970), 130–133
Presentations in Math-Net.Ru
1.
О предельной теореме Линдеберга-Феллера E. L. Presman, Sh. K. Formanov Principle Seminar of the Department of Probability Theory, Moscow State University May 15, 2019 16:45
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