2019
Том 71
№ 7

Buldygin V. V.

Articles: 26
Article (Russian)

Karamata theorem for regularly log-periodic functions

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.

Article (English)

On the convergence of positive increasing functions to infinity

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.

Obituaries (Ukrainian)

Anatolii Yakovych Dorogovtsev

Ukr. Mat. Zh. - 2004. - 56, № 8. - pp. 1151-1152

Anniversaries (Ukrainian)

Mykhailo Iosypovych Yadrenko (On His 70th Birthday)

Ukr. Mat. Zh. - 2002. - 54, № 4. - pp. 435-438

Article (English)

Properties of a Subclass of Avakumović Functions and Their Generalized Inverses

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.

Article (Ukrainian)

On the Asymptotic Properties of Solutions of Linear Stochastic Differential Equations in $R^d$

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.

Article (Russian)

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.

Article (Russian)

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.

Brief Communications (Ukrainian)

On the Levy-Baxter theorems for shot-noise fields. III

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.

Article (Ukrainian)

On the Levy-Baxter theorems for shot-noise fields. II

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.

Article (Ukrainian)

On the Levy-Baxter theorems for shot-noise fields. I

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.

Article (Ukrainian)

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.

Brief Communications (Ukrainian)

To the memory of Valentin Anatol'evich Zmorovich

Ukr. Mat. Zh. - 1994. - 46, № 8. - pp. 1110–1111

Article (Ukrainian)

Estimates of the supremum distribution for a certain class of random processes

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.

Article (Ukrainian)

Comparison theorems and asymptotic behavior of correlation estimators in spaces of continuous functions. II

Ukr. Mat. Zh. - 1991. - 43, № 5. - pp. 579-583

Article (Ukrainian)

Comparison theorems and asymptotic behavior of correlation estimates in spaces of continuous functions. I.

Ukr. Mat. Zh. - 1991. - 43, № 4. - pp. 482-489

Article (Ukrainian)

Asymptotic properties of correlation bounds in functional spaces. I.

Ukr. Mat. Zh. - 1991. - 43, № 2. - pp. 179–187

Article (Ukrainian)

A generalized summation of a random series

Ukr. Mat. Zh. - 1989. - 41, № 12. - pp. 1618–1623

Article (Ukrainian)

Convergence of Fourier series of stationary Gaussian processes

Ukr. Mat. Zh. - 1987. - 39, № 3. - pp. 278–282

Article (Ukrainian)

Cylindrical and Borel σ-algebras

Ukr. Mat. Zh. - 1986. - 38, № 1. - pp. 12–17

Article (Ukrainian)

Oscillation of the realizations of bounded almost-sure Gaussian sequences

Ukr. Mat. Zh. - 1985. - 37, № 1. - pp. 110 – 111

Article (Ukrainian)

Borel measures in nonseparable metric spaces

Ukr. Mat. Zh. - 1983. - 35, № 5. - pp. 552—556

Article (Ukrainian)

Convergence of the decomposition of a Gaussian field

Ukr. Mat. Zh. - 1982. - 34, № 2. - pp. 137-143

Article (Ukrainian)

Sub-Gaussian random variables

Ukr. Mat. Zh. - 1980. - 32, № 6. - pp. 723–730

Article (Ukrainian)

Sub-Gaussian processes and convergence of random series in functional spaces

Ukr. Mat. Zh. - 1977. - 29, № 4. - pp. 443–454

Article (Ukrainian)

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