Buldygin V. V.
Ukr. Mat. Zh. - 2012. - 64, № 11. - pp. 1443-1463
We generalize the Karamata theorem on the asymptotic behavior of integrals with variable limits to the class of regularly log-periodic functions.
Ukr. Mat. Zh. - 2010. - 62, № 10. - pp. 1299–1308
We study the conditions of convergence to infinity for some classes of functions extending the well-known class of regularly varying (RV) functions, such as, e.g., $O$-regularly varying (ORV) functions or positive increasing (PI) functions.
Ukr. Mat. Zh. - 2004. - 56, № 8. - pp. 1151-1152
Ukr. Mat. Zh. - 2002. - 54, № 4. - pp. 435-438
Ukr. Mat. Zh. - 2002. - 54, № 2. - pp. 149-169
We study properties of a subclass of ORV functions introduced by Avakumović and provide their applications for the strong law of large numbers for renewal processes.
Ukr. Mat. Zh. - 2000. - 52, № 9. - pp. 1166-1175
We investigate necessary and sufficient conditions for the almost-sure boundedness of normalized solutions of linear stochastic differential equations in $R^d$ their almost-sure convergence to zero. We establish an analog of the bounded law of iterated logarithm.
Strong Law of Large Numbers with Operator Normalizations for Martingales and Sums of Orthogonal Random Vectors
Ukr. Mat. Zh. - 2000. - 52, № 8. - pp. 1045-1061
We establish the strong law of large numbers with operator normalizations for vector martingales and sums of orthogonal random vectors. We describe its applications to the investigation of the strong consistency of least-squares estimators in a linear regression and the asymptotic behavior of multidimensional autoregression processes.
On asymptotic properties of the empirical correlation matrix of a homogeneous vector-valued Gaussian field
Ukr. Mat. Zh. - 2000. - 52, № 3. - pp. 300-318
We investigate properties of the empirical correlation matrix of a centered stationary Gaussian vector field in various function spaces. We prove that, under the condition of integrability of the square of the spectral density of the field, the normalization effect takes place for a correlogram and integral functional of it.
Ukr. Mat. Zh. - 1999. - 51, № 2. - pp. 251–254
We establish sufficient conditions for singularity of distributions of shot-noise fields with response functions of a certain form.
Ukr. Mat. Zh. - 1999. - 51, № 1. - pp. 12–31
We establish sufficient conditions under which shot-noise fields with a response function of a certain form possess the Levy-Baxter property on an increasing parametric set.
Ukr. Mat. Zh. - 1998. - 50, № 11. - pp. 1463–1476
We consider shot-noise fields generated by countably additive stochastically continuous homogeneous random measures with independent values on disjoint sets. We establish necessary and sufficient conditions under which the shot-noise fields possess the Levy-Baxter property on fixed and increasing parametric sets.
On asymptotic normality of estimates for correlation functions of stationary Gaussian processes in the space of continuous functions
Ukr. Mat. Zh. - 1995. - 47, № 11. - pp. 1485–1497
We establish conditions of the weak convergence of the empirical correlogram of a stationary Gaussian process to some Gaussian process in the space of continuous functions. We prove that such a convergence holds for a broad class of stationary Gaussian processes with square integrable spectral density.
On the properties of an empirical correlogram of a Gaussian process with square integrable spectral density
Ukr. Mat. Zh. - 1995. - 47, № 7. - pp. 876–889
We study properties of an empirical correlogram of a centered stationary Gaussian process. We prove that if the spectral density of the process is square integrable, then there is a normalization effect for the correlogram and integral functionals of it.
Baranovskii F. T., Berezansky Yu. M., Buldygin V. V., Daletskii Yu. L., Dobrovol'skii V. A., Dzyadyk V. K., Lozovik V. G., Mitropolskiy Yu. A., Samoilenko A. M., Skrypnik I. V., Tamrazov P. M., Yaremchuk F. P.
Ukr. Mat. Zh. - 1994. - 46, № 8. - pp. 1110–1111
Ukr. Mat. Zh. - 1993. - 45, № 5. - pp. 596–608
Exponential estimates of the “tails” of supremum distributions are obtained for a certain class of pre-Gaussian random processes. The results obtained are applied to the quadratic forms of Gaussian processes and to processes representable as stochastic integrals of processes with independent increments.
Comparison theorems and asymptotic behavior of correlation estimators in spaces of continuous functions. II
Ukr. Mat. Zh. - 1991. - 43, № 5. - pp. 579-583
Comparison theorems and asymptotic behavior of correlation estimates in spaces of continuous functions. I.
Ukr. Mat. Zh. - 1991. - 43, № 4. - pp. 482-489
Ukr. Mat. Zh. - 1991. - 43, № 2. - pp. 179–187
Ukr. Mat. Zh. - 1989. - 41, № 12. - pp. 1618–1623
Ukr. Mat. Zh. - 1987. - 39, № 3. - pp. 278–282
Ukr. Mat. Zh. - 1986. - 38, № 1. - pp. 12–17
Ukr. Mat. Zh. - 1985. - 37, № 1. - pp. 110 – 111
Ukr. Mat. Zh. - 1983. - 35, № 5. - pp. 552—556
Ukr. Mat. Zh. - 1982. - 34, № 2. - pp. 137-143
Ukr. Mat. Zh. - 1980. - 32, № 6. - pp. 723–730
Ukr. Mat. Zh. - 1977. - 29, № 4. - pp. 443–454
On the structure of a ?-algebra of borel sets and the convergence of certain stochastic series in Banach spaces
Ukr. Mat. Zh. - 1975. - 27, № 4. - pp. 435–442