limit theorems for stochastic processes and random fields,
dependence conditions for systems of random variables (mixing,
association etc.),
moment and maximal inequalities for sums of multi-indexed summands,
central limit theorem,
functional law of the iterated logarithm,
invariance principles,
rates of convergence in limit theorems,
Burgers' equation with random initial conditions,
stochastic models in radio-biology,
statistical methods of data analysis,
estimation of genetic risks of complex diseases.
Subject:
Limit theorems for stochastic processes and random fields and their applications. Stochastic models for dependent data. Statistical methods of genetic data analysis.
Main publications:
A. Bulinski, A. Shashkin, Limit Theorems for Associated Random Fields and Related Systems, Advanced Series on Statistical Science and Applied Probability, 10, World Scientific, Singapore, 2007, 436 pp.
A. V. Bulinski, A. N. Shiryaev, Theory of Stochastic Processes, Classical University Textbook, Fizmatlit, Moscow, 2005 (in Russian)
A. Bulinski, “A new variant of the functional law of the iterated logarithm”, Theory of Probability and its Applications, 25:3 (1981), 493–503
A. Bulinski, A. Shashkin, “Strong invariance principle for dependent random fields”, Dynamics and Stochastics, Festscrift in honor of M. S. Keane, IMS Lecture Notes – Monograph Series, 48, 2006, 128–143
A. Bulinski, O. Butkovsky, V. Sadovnichy, A. Shashkin, P. Yaskov, A. Balatskiy, L. Samokhodskaya, V. Tkachuk, “Statistical Methods of SNP Data Analysis and Applications”, Open Journal of Statistics, 2:1 (2012), 1–15
Alexander Bulinski, Evgeny Spodarev, Florian Timmermann, “Central limit theorems for the excursion set volumes of weakly dependent random fields”, Bernoulli, 18:1 (2012), 100–118
A. V. Bulinskii, S. A. Molchanov, “Asymptotic Gaussian property of the solution of the Burgers equation with random initial data”, Theory Probab. Appl., 36:2 (1991), 217–236
3.
Alexander Bulinski, Denis Dimitrov, “Statistical Estimation of the Shannon Entropy”, Acta Math. Sin., Engl. Ser., 35:1 (2019), 17–46
A. V. Bulinski, E. Shabanovich, “Asymptotical behaviour for some functionals of positively and negatively dependent random fields”, Fundam. Prikl. Mat., 4:2 (1998), 479–492
5.
A. V. Bulinski, “Rate of convergence in the central limit theorem for fields of associated random variables”, Theory Probab. Appl., 40:1 (1995), 136–144
6.
A. V. Bulinski, “Inequalities for the moments of sums of associated multi-indexed variables”, Theory Probab. Appl., 38:2 (1993), 342–349
7.
Alexander Bulinski, Denis Dimitrov, “Statistical estimation of the Kullback–Leibler divergence”, Mathematics, 9:5 (2021), 544 , 36 pp. ;
A. Bulinski, O. Butkovsky, V. Sadovnichy, A. Shashkin, P. Yaskov, A. Balatskiy, L. Samokhodskaya, V. Tkachuk, “Statistical methods of SNP data analysis and applications”, Open J. Stat., 2:1 (2012), 73–87
A. V. Bulinski, “The functional law of the iterated logarithm for associated random fields”, Fundam. Prikl. Mat., 1:3 (1995), 623–639
14.
A. V. Bulinskiǐ, A. N. Kolmogorov, “Linear sampling estimations of sums”, Theory Probab. Appl., 24:2 (1979), 241–252
15.
A. V. Bulinskiǐ, I. G. Žurbenko, “A central limit theorem for additive random functions”, Theory Probab. Appl., 21:4 (1977), 687–697
16.
A. V. Bulinski, “Conditional central limit theorem”, Theory Probab. Appl., 61:4 (2017), 613–631
17.
A. V. Bulinski, “To the foundation of the dimensionality reduction method for explanatory variables”, J. Math. Sci. (N. Y.), 199:2 (2014), 113–122
18.
Alexander Bulinski, Alexey Kozhevin, “Statistical estimation of mutual information for mixed model”, Methodol. Comput. Appl. Probab., 23 (2021), 123–142;
A. V. Bulinskii, “The CLT for shot-noise fields”, J. Soviet Math., 61:1 (1992), 1840–1845
24.
A. V. Bulinski, “On relevant features selection based on information theory”, Theory Probab. Appl., 68:3 (2023), 392–410
25.
A. V. Bulinski, M. A. Lifshits, “Rate of convergence in the functional law of the iterated logarithm with non-standard normalizing factors”, Russian Math. Surveys, 50:5 (1995), 925–944
26.
A. V. Bulinskiǐ, “On a class of optimal estimators of sums of random variables”, Theory Probab. Appl., 28:2 (1984), 419–425
27.
A. V. Bulinski, “Estimate of the interaction neighborhood radius for a Markov random field”, Theory Probab. Appl., 60:2 (2016), 313–318
28.
A. Bulinski, “Central limit theorem related to MDR-method”, Asymptotic laws and methods in stochastics, Fields Inst. Commun., 76, Fields Inst. Res. Math. Sci., Toronto, ON, 2015, 113–128
A. V. Bulinski, A. S. Rakitko, “Estimation of nonbinary random response”, Dokl. Math., 89:2 (2014), 225–229
31.
Alexander Bulinski, Evgeny Spodarev, “Introduction to random fields”, Stochastic geometry, spatial statistics and random fields, Lect. Notes Math., 2068, Springer, Heidelberg, 2013, 277–335
A. V. Bulinski, S. V. Dil'man, “Universal normalization in the law of the iterated logarithm”, Russian Math. Surveys, 57:2 (2002), 418–419
33.
A. V. Bulinski, M. A. Lifshits, “Rates of clustering in Strassen's law for random polygons”, J. Math. Sci. (New York), 93:3 (1999), 287–293
34.
A. V. Bulinskii, N. V. Verdenskaya, “An Estimate of the Convergence Rate in the Functional Law of the Iterated Logarithm”, Theory Probab. Appl., 32:2 (1987), 334–337
35.
A. V. Bulinski, “On the rate of convergence in the functional law of the iterated logarithm”, Dokl. Akad. Nauk SSSR, 263:2 (1982), 274–276
36.
A. V. Bulinski, “On the functional law of the iterated logarithm”, Dokl. Akad. Nauk SSSR, 238:5 (1978), 1025–1027
37.
Alexander Bulinski, “Some statistical methods in genetics”, Stochastic geometry, spatial statistics and random fields, Lect. Notes Math., 2120, Springer, Cham, 2014, 293–320
38.
A. V. Bulinski, M. R. Usmanov, “A remark on moment inequalities for a sequence of associated variables”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1992, no. 5, 72–73
39.
A. V. Bulinskij, “An estimate for the rate of convergence in the central limit theorem for random fields”, Dokl. Akad. Nauk SSSR, 291:1 (1986), 22–25
40.
A. V. Bulinskii, “Analogs of Mann–Whitney statistics in an experiment with symmetric randomization”, Theory Probab. Appl., 29:4 (1985), 795–798
41.
A. V. Bulinski, “Measures of dependence that are close to the maximum correlation coefficient”, Dokl. Akad. Nauk SSSR, 277:6 (1984), 1296–1298
42.
A. V. Bulinski, O. I. Shipilov, “On the Mann–Whitney statistic in an experiment with randomization”, Dokl. Akad. Nauk SSSR, 269:4 (1983), 789–792
43.
A. V. Bulinski, “On a form of the invariance principle”, Dokl. Akad. Nauk SSSR, 267:1 (1982), 22–26
44.
A. V. Bulinski, “Linear estimators of sums of random variables”, Dokl. Akad. Nauk SSSR, 255:4 (1980), 784–789
45.
A. V. Bulinski, “The central limit theorem for random fields with strong and weak dependence”, Dokl. Akad. Nauk SSSR, 248:1 (1979), 17–19
46.
A. V. Bulinski, “On the speed of convergence in the central limit theorem for additive random functions”, Dokl. Akad. Nauk SSSR, 235:4 (1977), 741–744
47.
A. V. Bulinski, I. G. Zhurbenko, “The central limit theorem for random fields”, Dokl. Akad. Nauk SSSR, 226:1 (1976), 23–25
48.
A. V. Bulinski, “Estimations of semi-invariants and high-order covariances of bounded random variables”, Theory Probab. Appl., 19:4 (1975), 835–839
49.
A. V. Bulinski, “Stability properties of feature selection measures”, Theory Probab. Appl., 69:1 (2024), 25–34
50.
Al. V. Bulinski, “On an example of expectation evaluation”, Theory Probab. Appl., 69:2 (2024), 313–321
51.
G. G. Amosov, Al. V. Bulinski, An. V. Bulinski, V. M. Buchstaber, I. A. Ibragimov, V. P. Maslov, A. Ya. Helemskii, A. M. Chebotarev, M. E. Shirokov, A. N. Shiryaev, “Alexander Semenovich Holevo (on his 75th birthday)”, Russian Math. Surveys, 73:6 (2018), 1131–1136
52.
A. V. Bulinski, M. A. Vronskii, “Information about meeting of Shyryaev seminar (1999)”, Theory Probab. Appl., 44:3 (2000), 622–631
53.
A. A. Borovkov, Al. V. Bulinski, A. M. Vershik, D. Zaporozhets, A. S. Holevo, A. N. Shiryaev, “Ildar Abdullovich Ibragimov (on his ninetieth birthday)”, Russian Math. Surveys, 78:3 (2023), 573–583
Метод Стейна и его развитие Al. V. Bulinski Principle Seminar of the Department of Probability Theory, Moscow State University September 14, 2022 16:45
The central limit theorem for random fields Al. V. Bulinski Traditional winter session MIAN–POMI devoted to the topic "Probability and Functional Analysis" February 16, 2012 15:00