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
A. V. Bulinski, “Stability properties of feature selection measures”, Theory Probab. Appl., 69:1 (2024), 25–34
2.
Al. V. Bulinski, “On an example of expectation evaluation”, Theory Probab. Appl., 69:2 (2024), 313–321
2023
3.
A. V. Bulinski, “On relevant features selection based on information theory”, Theory Probab. Appl., 68:3 (2023), 392–410
4.
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
2021
5.
Alexander Bulinski, Alexey Kozhevin, “Statistical estimation of mutual information for mixed model”, Methodol. Comput. Appl. Probab., 23 (2021), 123–142;
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
2017
10.
Alexander Bulinski, Alexey Kozhevin, “New version of the MDR method for stratified samples”, Stat. Optim. Inf. Comput., 5:1 (2017), 1–18
A. V. Bulinski, “Conditional central limit theorem”, Theory Probab. Appl., 61:4 (2017), 613–631
2016
12.
A. V. Bulinski, “Estimate of the interaction neighborhood radius for a Markov random field”, Theory Probab. Appl., 60:2 (2016), 313–318
2015
13.
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
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. 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, “To the foundation of the dimensionality reduction method for explanatory variables”, J. Math. Sci. (N. Y.), 199:2 (2014), 113–122
2012
21.
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. Bulinski, “Statistical Version of the Central Limit Theorem for Vector-Valued Random Fields”, Math. Notes, 76:4 (2004), 455–464
2002
23.
A. V. Bulinski, S. V. Dil'man, “Universal normalization in the law of the iterated logarithm”, Russian Math. Surveys, 57:2 (2002), 418–419
2000
24.
A. V. Bulinski, M. A. Vronskii, “Information about meeting of Shyryaev seminar (1999)”, Theory Probab. Appl., 44:3 (2000), 622–631
1998
25.
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
1997
26.
Yu. Yu. Bakhtin, A. V. Bulinski, “Moment inequalities for sums of dependent multiindexed random variables”, Fundam. Prikl. Mat., 3:4 (1997), 1101–1108
1996
27.
A. V. Bulinski, M. A. Vronskii, “Statistical variant of the CLT for associated random fields”, Fundam. Prikl. Mat., 2:4 (1996), 999–1018
1999
28.
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
1995
29.
A. V. Bulinski, “The functional law of the iterated logarithm for associated random fields”, Fundam. Prikl. Mat., 1:3 (1995), 623–639
30.
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
31.
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
1993
32.
A. V. Bulinski, “Inequalities for the moments of sums of associated multi-indexed variables”, Theory Probab. Appl., 38:2 (1993), 342–349
1992
33.
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
1991
34.
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
1992
35.
A. V. Bulinskii, “The CLT for shot-noise fields”, J. Soviet Math., 61:1 (1992), 1840–1845
1987
36.
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
1986
37.
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
1985
38.
A. V. Bulinskii, “Analogs of Mann–Whitney statistics in an experiment with symmetric randomization”, Theory Probab. Appl., 29:4 (1985), 795–798
1984
39.
A. V. Bulinski, “Measures of dependence that are close to the maximum correlation coefficient”, Dokl. Akad. Nauk SSSR, 277:6 (1984), 1296–1298
40.
A. V. Bulinskiǐ, “On a class of optimal estimators of sums of random variables”, Theory Probab. Appl., 28:2 (1984), 419–425
1983
41.
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
1982
42.
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
43.
A. V. Bulinski, “On a form of the invariance principle”, Dokl. Akad. Nauk SSSR, 267:1 (1982), 22–26
1981
44.
A. V. Bulinskiǐ, “A new variant of the functional law of the iterated logarithm”, Theory Probab. Appl., 25:3 (1981), 493–503
1980
45.
A. V. Bulinski, “Linear estimators of sums of random variables”, Dokl. Akad. Nauk SSSR, 255:4 (1980), 784–789
1979
46.
A. V. Bulinskiǐ, A. N. Kolmogorov, “Linear sampling estimations of sums”, Theory Probab. Appl., 24:2 (1979), 241–252
47.
A. V. Bulinski, “The central limit theorem for random fields with strong and weak dependence”, Dokl. Akad. Nauk SSSR, 248:1 (1979), 17–19
1978
48.
A. V. Bulinski, “On the functional law of the iterated logarithm”, Dokl. Akad. Nauk SSSR, 238:5 (1978), 1025–1027
49.
A. V. Bulinskiǐ, “Remarks on the normalization in the law of the iterated logarithm”, Theory Probab. Appl., 22:2 (1978), 398–399
1977
50.
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
51.
A. V. Bulinskiǐ, I. G. Žurbenko, “A central limit theorem for additive random functions”, Theory Probab. Appl., 21:4 (1977), 687–697
1976
52.
A. V. Bulinski, I. G. Zhurbenko, “The central limit theorem for random fields”, Dokl. Akad. Nauk SSSR, 226:1 (1976), 23–25
1975
53.
A. V. Bulinski, “Estimations of semi-invariants and high-order covariances of bounded random variables”, Theory Probab. Appl., 19:4 (1975), 835–839
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
2024
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