2019
Том 71
№ 11

# Shurenkov V. M.

Articles: 16
Article (Ukrainian)

### Asymptotic representation of the perron root of a matrix-valued stochastic evolution

Ukr. Mat. Zh. - 1996. - 48, № 1. - pp. 35-43

We study an asymptotic representation of the Perron root of a matrix-valued stochastic evolution given by the transport equation.

Article (Ukrainian)

### Some properties of random evolutions

Ukr. Mat. Zh. - 1995. - 47, № 10. - pp. 1333-1337

We study asymptotic properties of matrix-valued random evolutions and consider an example of evolutions of this type.

Brief Communications (Russian)

### Remark on the central limit theorem for ergodic chains

Ukr. Mat. Zh. - 1995. - 47, № 1. - pp. 118-120

We obtain sufficient conditions that should be imposed on a functionf in order that, for ergodic Markov chains, the sum $$\frac{1}{{\sqrt n }} \sum\limits_{k = 0}^{n - 1} { f(X_k )}$$ be asymptotically normal.

Brief Communications (Russian)

### Matrix infinite-dimensional analog of the Wiener theorem on local inversion of Fourier transforms

Ukr. Mat. Zh. - 1995. - 47, № 1. - pp. 141-145

A matrix infinite-dimensional analog of the Wiener theorem on local inversion of Fourier transforms is proved.

Brief Communications (Russian)

### Central limit theorem for stochastically additive functionals of ergodic chains

Ukr. Mat. Zh. - 1994. - 46, № 10. - pp. 1421–1423

A central limit theorem is proved for stochastically additive functional of ergodic Markov chains.

Brief Communications (Russian)

### Central limit theorem for special classes of functions of ergodic chains

Ukr. Mat. Zh. - 1994. - 46, № 8. - pp. 1092–1094

A central limit theorem is proved for E-finite bounded functions of ergodic Markov chains. Two useful corollaries are presented.

Brief Communications (Ukrainian)

### On potentials of ergodic Markov chains

Ukr. Mat. Zh. - 1994. - 46, № 4. - pp. 446–449

Two theorems on the existence of the potential of an ergodic Markov chain in an arbitrary phase space are proved.

Brief Communications (Russian)

### Central limit theorem for centered frequencies of a countable ergodic markov chain

Ukr. Mat. Zh. - 1993. - 45, № 12. - pp. 1713–1715

On the basis of results relating to the behavior of the potential of a countable ergodic Markov chain, for a certain class of functions, the asymptotic normality of a variable $\cfrac{1}{\sqrt{n}}\sum^{n-1}_{k=0}f(X_k)$ for $n \rightarrow \infty$ has been proved. The asymptotic normality of the centering frequencies has been obtained without using the finileness conditions for the time $M_0\tau^2$ of the first return into a chain state.

Article (Russian)

### On asymptotics of the potential of a countable ergodic Markov chain

Ukr. Mat. Zh. - 1993. - 45, № 2. - pp. 265–269

For a class of functions $f$, the convergence in Abel's sense is proved for the potential \$\sum_{n⩾o}P^nf(i) of a uniform ergodic Markov chain in a countable phase space. Several corollaries are obtained which are useful from the point of view of the possible application to CLT (the central limit theorem) for Markov chains. In particular, we establish the condition equivalent to the boundedness of the second moment for the time of the first return into the state.

Article (Ukrainian)

### Asymptotic behavior of terminating markov processes, near to ergodic

Ukr. Mat. Zh. - 1990. - 42, № 12. - pp. 1701–1703

Article (Ukrainian)

### Limit distribution of the position of a semicontinuous process with negative infinite mean at the moment of exit from an interval

Ukr. Mat. Zh. - 1988. - 40, № 4. - pp. 538–541

Article (Ukrainian)

### Time of exit of a semicontinuous process with boundary

Ukr. Mat. Zh. - 1986. - 38, № 5. - pp. 625–629

Article (Ukrainian)

### Limit distribution of position at the moment a complex poisson process with zero mean and infinite variance leaves an interval

Ukr. Mat. Zh. - 1981. - 33, № 4. - pp. 552-557

Article (Ukrainian)

### Limit distribution of the position of a semicontinuous process with independent increments with zero mean and infinite dispersion at the moment of exit from an interval

Ukr. Mat. Zh. - 1980. - 32, № 2. - pp. 262 - 264

Article (Ukrainian)

### Limit distributions of time averages for a semi-Markov process with finite number of states

Ukr. Mat. Zh. - 1979. - 31, № 5. - pp. 598–603

Article (Ukrainian)

### The potential method in boundaey-value problems foe bandom walks on Markov chains

Ukr. Mat. Zh. - 1977. - 29, № 4. - pp. 464–471