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
G. G. Amosov, A. V. Bulinski, A. V. Bulinski, V. M. Buchstaber, I. A. Ibragimov, V. P. Maslov, A. Ya. Helemskii, A. M. Chebotarev, M. E. Shirokov, A. N. Shiryaev, Uspekhi Mat. Nauk
2017
2.
Alexander Bulinski, Alexey Kozhevin, “New version of the MDR method for stratified samples”, Stat. Optim. Inf. Comput., 5:1 (2017), 1–18
3.
A. V. Bulinski, “Conditional central limit theorem”, Theory Probab. Appl., 61:4 (2017), 613–631
2016
4.
A. V. Bulinski, “Estimate of the interaction neighborhood radius for a Markov random field”, Theory Probab. Appl., 60:2 (2016), 313–318
2015
5.
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
6.
Alexander Bulinski, Alexander Rakitko, “MDR method for nonbinary response variable”, J. Multivariate Anal., 135 (2015), 25–42
2014
7.
Alexander Bulinski, “Some statistical methods in genetics”, Stochastic geometry, spatial statistics and random fields, Lect. Notes Math., 2120, Springer, Cham, 2014, 293–320
8.
A. V. Bulinski, A. S. Rakitko, “Estimation of nonbinary random response”, Dokl. Math., 89:2 (2014), 225–229
2013
9.
Alexander Bulinski, Evgeny Spodarev, “Central limit theorems for weakly dependent random fields”, Stochastic geometry, spatial statistics and random fields, Lect. Notes Math., 2068, Springer, Heidelberg, 2013, 337–383
10.
Alexander Bulinski, Evgeny Spodarev, “Introduction to random fields”, Stochastic geometry, spatial statistics and random fields, Lect. Notes Math., 2068, Springer, Heidelberg, 2013, 277–335
2012
11.
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
2014
12.
A. V. Bulinski, “To the foundation of the dimensionality reduction method for explanatory variables”, J. Math. Sci. (N. Y.), 199:2 (2014), 113–122 (cited: 5)
2012
13.
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
2004
14.
A. V. Bulinski, “Statistical Version of the Central Limit Theorem for Vector-Valued Random Fields”, Math. Notes, 76:4 (2004), 455–464 (cited: 5) (cited: 4)
2002
15.
A. V. Bulinski, S. V. Dil'man, “Universal normalization in the law of the iterated logarithm”, Russian Math. Surveys, 57:2 (2002), 418–419 (cited: 1)
2000
16.
A. V. Bulinski, M. A. Vronskii, “Information about meeting of Shyryaev seminar (1999)”, Theory Probab. Appl., 44:3 (2000), 622–631
1998
17.
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
18.
Yu. Yu. Bakhtin, A. V. Bulinski, “Moment inequalities for sums of dependent multiindexed random variables”, Fundam. Prikl. Mat., 3:4 (1997), 1101–1108
1996
19.
A. V. Bulinski, M. A. Vronskii, “Statistical variant of the CLT for associated random fields”, Fundam. Prikl. Mat., 2:4 (1996), 999–1018
1999
20.
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
21.
A. V. Bulinski, “The functional law of the iterated logarithm for associated random fields”, Fundam. Prikl. Mat., 1:3 (1995), 623–639
22.
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 (cited: 3)
23.
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 (cited: 7)
1993
24.
A. V. Bulinski, “Inequalities for the moments of sums of associated multi-indexed variables”, Theory Probab. Appl., 38:2 (1993), 342–349 (cited: 7)
1991
25.
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 (cited: 34)
1992
26.
A. V. Bulinskii, “The CLT for shot-noise fields”, J. Soviet Math., 61:1 (1992), 1840–1845
1987
27.
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
1985
28.
A. V. Bulinskii, “Analogs of Mann–Whitney statistics in an experiment with symmetric randomization”, Theory Probab. Appl., 29:4 (1985), 795–798
1984
29.
A. V. Bulinskiǐ, “On a class of optimal estimators of sums of random variables”, Theory Probab. Appl., 28:2 (1984), 419–425
1981
30.
A. V. Bulinskiǐ, “A new variant of the functional law of the iterated logarithm”, Theory Probab. Appl., 25:3 (1981), 493–503 (cited: 3)
1979
31.
A. V. Bulinskiǐ, A. N. Kolmogorov, “Linear sampling estimations of sums”, Theory Probab. Appl., 24:2 (1979), 241–252 (cited: 9)
1978
32.
A. V. Bulinskiǐ, “Remarks on the normalization in the law of the iterated logarithm”, Theory Probab. Appl., 22:2 (1978), 398–399
1977
33.
A. V. Bulinskiǐ, I. G. Žurbenko, “A central limit theorem for additive random functions”, Theory Probab. Appl., 21:4 (1977), 687–697
1976
34.
A. V. Bulinski, I. G. Zhurbenko, “The central limit theorem for random fields”, Dokl. Akad. Nauk SSSR, 226:1 (1976), 23–25
1975
35.
A. V. Bulinski, “Estimations of semi-invariants and high-order covariances of bounded random variables”, Theory Probab. Appl., 19:4 (1975), 835–839
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
2017
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