Prof. Igor Borisov

sibam@math.nsc.ru
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  • Date of birth: November 10, 1951
  • Positions:
    Top-level Research Fellow, Laboratory of Probability Theory and Mathematical Statistics, Sobolev Institute of Mathematics, Novosibirsk, Russia;
    Professor, Chair of Probability Theory and Mathematical Statistics, Novosibirsk State University, Novosibirsk, Russia
  • Education and degrees:
    1969-1974, Novosibirsk State University, Mathematical Department
    1974-1978, Post Graduate Course, Sobolev Institute of Mathematics
    1978, Candidate of Science (Ph.D), Sobolev Institute of Mathematics
    1988, Doctor of Science, Steklov Mathematical Institute
    1991, Professor

Ph.D. Students (Candidates of Science)

  • Evgenii Soloviov (1993)
  • Pavel Ruzankin (2001)
  • Dmitrii Mironov (2001)
  • Evgenii Baklanov (2002)
  • Nikolai Arkashov (2005)
  • Alexandr Bystrov (2006)
  • Nadezhda Volodko (2008)
  • Dmitrii Sidorov (2010)
  • Sergei Khrushchev (2015)
  • Vasilii Zhechev (2018)
  • Evgenii Shefer (2021)

    Teaching Materials

  • Lectures for students of Mathematical Department, NSU [in Russian]: Probability, Statistics
  • Course for graduate students of Mathematical Department, NSU [in English]: PoisGauss

    Selected publications

  • Yu.Yu. Linke, I.S.Borisov. Insensitivity of Nadaraya--Watson estimators to design correlation. Communications in Statistics - Theory and Methods. (2021)
  • I. S. Borisov, Yu. Yu. Linke, P. S. Ruzankin. Universal weighted kernel-type estimators for some class of regression models. Metrika, 84:2 (2021), 141-166.
  • I. S. Borisov, E. I. Shefer. Asymptotic behavior of the distribution tail of the sojourn time for a random walk in a domain of moderate large deviations. Siberian Adv. Math., 30:3 (2020), 162-176.
  • P. S. Ruzankin, I. S. Borisov. On the rate of Poisson approximation to Bernoulli partial sum processes. Statist. Probab. Letters, 162 (2020), 108754.
  • I. S. Borisov, E. I. Shefer. Asymptotic behavior of the mean sojourn time for a random walk in a domain of large deviations. Siberian Adv. Math., 30:2 (2020), 77-90.
  • Yu. Yu. Linke, I. S. Borisov. Toward the notion of intrinsically linear models in nonlinear regression. Siberian Adv. Math., .29:3 (2019), 210-216.
  • I. S. Borisov, A. A. Bystrov. Exponential inequalities for the distributions of canonical multiple partial sum processes. Theory Probab. Appl., 64:2 (2019), 171-175.
  • I. S. Borisov, V. A. Zhechev. Exponential inequalities for the distributions of V-processes based on dependent observations. Siberian Adv. Math., 29:4 (2019), 263-273.
  • I. S. Borisov, E. I. Shefer. The asymptotic behavior of the mean sojourn time for a random walk above a receding curvilinear boundary. J. Math. Scien., 237 (2019), 511-520.
  • Yu. Yu. Linke, I. S. Borisov. Constructing explicit estimators in nonlinear regression models. Teor. Veroyatnost. i Primenen., 63:1 (2018), 29-56
  • Yu. Yu. Linke, I. S. Borisov. Constructing initial estimators in one-step estimation procedures of nonlinear regression. Stat. Probab. Lett., 120 (2017), 87-94
  • I. S. Borisov. The rate of convergence in Hoeffding's theorem and some applications. Statist. Probab. Lett., 109 (2016) 99-105.
  • I. S. Borisov, N. V. Volod'ko. Asymptotic expansions for the distributions of canonical V-statistics of third order. Teor. Veroyatnost. i Primenen., 60:1 (2015), 3-24.
  • I. S. Borisov, N. V. Volodko. A note on exponential inequalities for the distribution tails of canonical von Mises' statistics of dependent observations. Stat. Probab. Lett., 96 (2015), 287-291.
  • I. S. Borisov. A note on a result by W. Hoeffding. Stat. Probab. Lett., 87 (2014), 7-11.
  • I. S. Borisov, S. E. Khrushchev. Multiple stochastic integrals constructed by special expansions of products of the integrating stochastic processes. Mat. Tr., 17:2 (2014), 61-83.
  • I. S. Borisov. On the sum of the variances of the order statistics for samples of dependent observations. Sib. Elektron. Mat. Izv., 11 (2014), 857-862.
  • I. S. Borisov, V. A. Zhechev. Invariance principle for canonical U- and V-statistics based on dependent observations. Mat. Tr., 16:2 (2013), 28-44
  • I. S. Borisov. Stability of the partial sum process of residuals in a multiple linear regression model. Sib. Elektron. Mat. Izv., 10 (2013), 727-732.
  • I. S. Borisov. Transformations of the simplest nonsymmetric random walks and some applications of the invariance principle. Teor. Veroyatnost. i Primenen., 58:2 (2013), 381-387.
  • I. S. Borisov, S. E. Khrushchev. Constructing multiple stochastic integrals on non-Gaussian product measures. Mat. Tr., 15:2 (2012), 37-71.
  • I. S. Borisov, A. M. Shoisoronov. A continuity theorem in the ruin problem. Sibirsk. Mat. Zh., 52:4 (2011), 765-776.
  • I. S. Borisov, V. A. Zhechev. The functional limit theorem for the canonical U-processes defined on dependent trials. Sibirsk. Mat. Zh., 52:4 (2011), 754-764.
  • I. S. Borisov, N. N. Nikitina. Distribution of the number of crossings of a strip by trajectories of the simpliest random walks and a Wiener process with drift. Teor. Veroyatnost. i Primenen., 56:1 (2011), 152-158.
  • I. S. Borisov, D. I. Sidorov. Limit theorems for additive statistics based on moving average samples. Mat. Tr., 13:2 (2010), 10-32.
  • I. S. Borisov, N. V. Volodko. Limit theorems and exponential inequalities for the distributions of canonical U- and V-statistics of dependent trials. High Dimensional Probability, IMS Collections, , 5 (2009), 108-130.
  • I. S. Borisov, N. V. Volodko. Exponential inequalities for the distributions of canonical U- and V-statistics of dependent observations. Mat. Tr., 11:2 (2008), 3-19.
  • I. S. Borisov, N. V. Volodko. Orthogonal series and limit theorems for canonical U- and V-statistics of stationarily connected observations. Mat. Tr., 11:1 (2008), 25-48.
  • I. S. Borisov, I. S. Vorozheikin. Accuracy of approximation in the Poisson theorem in terms of the chi^2-distance. Sibirsk. Mat. Zh., 49:1 (2008), 8-22.
  • I. S. Borisov. A note on the distribution of the number of crossings of a strip by a random walk. Teor. Veroyatnost. i Primenen., 53:2 (2008), 345-349.
  • N. S. Arkashov, I. S. Borisov, A. A. Mogul'skii. Large deviation principle for partial sum processes of moving averages. Teor. Veroyatnost. i Primenen., 52:2 (2007), 209-239.
  • I. S. Borisov, A. A. Bystrov. Stochastic integrals and asymptotic analysis of canonical Von Mises statistics based on dependent observations. Lecture Notes Monograph Ser., 51 (2006), 1-17.
  • I. S. Borisov, A. A. Bystrov. Limit theorems for the canonical von Mises statistics with dependent data Sibirsk. Mat. Zh., 47:6 (2006), 1205-1217.
  • I. S. Borisov, A. A. Bystrov. Constructing a stochastic integral of a nonrandom function without orthogonality of the noise. Teor. Veroyatnost. i Primenen., 50:1 (2005), 52-80.
  • N. S. Arkashov, I. S. Borisov. Gaussian approximation to the partial sum processes of moving averages. Sibirsk. Mat. Zh., 45:6 (2004), 1221-1255.
  • I. S. Borisov, D. V. Mironov. Convergence rate of the distributions of normalized maximum likelihood estimators for irregular parametric families. Sibirsk. Mat. Zh., 44:3 (2003), 521-541.
  • I. S. Borisov. A note on Dobrushin's theorem and couplings in Poisson approximation in Abelian groups. Teor. Veroyatnost. i Primenen., 48:3 (2003), 576-583.
  • I. S. Borisov. Moment inequalities connected with accompanying Poisson laws in Abelian groups. Inter. J. of Math. and Math. Sciences., 44 (2003), 2771-2786.
  • E. A. Baklanov, I. S. Borisov. Probability inequalities and limit theorems for generalized L-statistics. Lit. Mat. Sb., 43:2 (2003), 149-168.
  • I. S. Borisov, P. S. Ruzankin. Poisson approximation for moments of unbounded functions of sums of independent random variables. Ann. Probab., 30:4 (2002), 1657-1680.
  • I. S. Borisov, L. A. Sakhanenko. The central limit theorem for generalized canonical von Mises statistics. Mat. Tr., 4:1 (2001), 3-17;Siberian Adv. Math., 10:4 (2000).
  • I. S. Borisov, D. V. Mironov. An asymptotic representation of the likelihood ratio for irregular families of distributions in the multivariate case. Sibirsk. Mat. Zh., 42:2 (2001), 275-288.
  • I. S. Borisov, E. A. Baklanov. Probability inequalities for generalized L-statistics. Sibirsk. Mat. Zh., 42:2 (2001), 258-274.
  • I. S. Borisov, D. V. Mironov. An asymptotic representation for the likelihood ratio for multidimensional samples with discontinuous densities. Teor. Veroyatnost. i Primenen., 45:2 (2000), 345-356.
  • I. S. Borisov, E. A. Baklanov. Moment inequalities for generalized L-statistics. Sibirsk. Mat. Zh., 39:3 (1998), 483-489.
  • I. S. Borisov. A note on Poisson approximation of rescaled set-indexed empirical processes. Statist. Probab. Letters, 46:1 (2000), 101-103.
  • I. S. Borisov, D. A. Panchenko, G.I. Skilyagina. On minimal smoothness conditions for asymptotic expansions of moments in the CLT. Siberian Adv.Math., 8:1 (1998).
  • I. S. Borisov, D. A. Panchenko. On consistency of the Maximum Spacing Estimators. Siberian Adv.Math., 7:3 (1997).
  • I. S. Borisov. Poisson approximation of the partial sum processes in Banach spaces. Sibirsk. Mat. Zh., 37:4 (1996), 723-731.
  • I. S. Borisov, G. I. Skilyagina. On asymptotic expansion of the moments of smooth functions in the central limit theorem. Sibirsk. Mat. Zh., 37:3 (1996), 519-525.
  • I. S. Borisov, A. V. Shadrin. Some remarks on the Sh. S. Ebralidze inequality. Teor. Veroyatnost. i Primenen., 41:1 (1996), 177-181.
  • I. S. Borisov. Bounds for characteristic functions of additive functionals of some Markov processes. Siberian Adv.Math., 6:4 (1996).
  • I. S. Borisov. Bounds for characteristic functions of additive functionals of order statistics. Siberian Adv.Math., 5:1 (1995).
  • I. S. Borisov. Strong Poisson and mixed approximations of sums of independent random variables in Banach spaces. Siberian Adv.Math., 3:2 (1993).
  • I. S. Borisov, E.A. Solov'ev. Second-order approximation for distributions of smooth functionals. Siberian Adv.Math., 2:2 (1992); Trudy Inst. Math., 20 (1993).
  • I. S. Borisov. Approximation for distributions of smooth functionals of sums of i.i.d. random variables in Banach spaces. Siberian Adv.Math., 1:1 (1991).
  • I. S. Borisov. Approximation for the distributions of Mises' statistics with multivariate kernels. Sibirsk. Mat. Zh. 32:4 (1991).
  • I. S. Borisov. Exponential inequalities for the distributions of von Mises and U-statistics. Proceedings of V-th Vilnius conf. (1989).
  • I. S. Borisov. Approximation for the distributions of smooth functionals of sums of independent random elements in Banach spaces. Trudy Inst. Math., 13 (1989).
  • I. S. Borisov. An accuracy of Gaussian approximation of the sum distribution of independent random variables in Banach spaces. Lecture Notes in Math., 1299 (1988).
  • I. S. Borisov. Upper and lower estimates of convergence rate in the invariance principle for empirical measures. Proceedings of IV-th Vilnius conf. (1987).
  • I. S. Borisov, A. A. Borovkov. The second-order approximation of random polygons in the Donsker-Prohorov invariance principle. Teor. Veroyatnost. i Primenen., 31:2 (1986), 225-245.
  • I. S. Borisov. Exponentional estimates for the distibutions of sums of independent random fields. Sibirsk. Mat. Zh., 26:1 (1985).
  • I. S. Borisov. A new approach to the problem of approximation for the distributions of sums of independent random variables in linear spaces. Trudy Inst. Math., 5 (1985).
  • I. S. Borisov. An approach to the problem of approximation for the distributions of sum of independent random elements. Doclady AN SSSR, 272:2 (1983).
  • I. S. Borisov. On the rate of convergence in Donsker–Prohorov invariance principle. Teor. Veroyatnost. i Primenen., 28:2 (1983), 367-372.
  • I. S. Borisov. On the rate of approximation in the central limit theorem for empirical processes. Sibirsk. Mat. Zh., 24:6 (1983).
  • I. S. Borisov. On a criterion for Gaussian random processes to be Markov ones. Teor. Veroyatnost. i Primenen., 27:4 (1982), 802-805.
  • I. S. Borisov. Approximation of empirical fields based on vector-valued observations with dependent coordinates. Sibirsk. Mat. Zh., 23:5 (1982).
  • I. S. Borisov. On conditions for the existence of bounded density of additive functionals for some random processes. Teor. Veroyatnost. i Primenen., 25:3 (1980), 464-475.
  • I. S. Borisov, A. A. Borovkov. Asymptotic behaviour of the number of nonoccupied channels for systems with refusals. Teor. Veroyatnost. i Primenen., 25:3 (1980), 449-463.
  • I. S. Borisov. Limit theorems for sums of dependent stochastic processes. Sibirsk. Mat. Zh., 20:2 (1979).
  • I. S. Borisov. Rate of convergence of the distributions of additive funtionals of a sequence of random variables. Sibirsk. Mat. Zh., 19:3 (1978).
  • I. S. Borisov. On the rate of convergence in the conditional invariance principle. Teor. Veroyatnost. i Primenen., 23:1 (1978), 67-79.
  • I. S. Borisov. On the rate of convergence for the distributions of integral type functionals. Teor. Veroyatnost. i Primenen., 21:2 (1976), 293-308.
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