2019
Том 71
№ 10

All Issues

Gasanenko V. A.

Articles: 12
Brief Communications (Russian)

Rarefaction of moving diffusion particles

Gasanenko V. A., Roitman A. B.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 5. - pp. 691-694

We investigate a flow of particles moving along a tube together with gas. The dynamics of particles is determined by a stochastic differential equation with different initial states. The walls of the tube absorb particles. We prove that if the incoming flow of particles is determined by a random Poisson measure, then the number of remained particles is characterized by the Poisson distribution. The parameter of this distribution is constructed by using a solution of the corresponding parabolic boundary-value problem.

Article (Russian)

On the Asymptotics of the Sojourn Probability of a Poisson Process between Two Nonlinear Boundaries That Move Away from One Another

Gasanenko V. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 1. - pp. 14-22

We obtain the complete asymptotic decomposition of the sojourn probability of a homogeneous Poisson process inside a domain with curvilinear boundaries. The coefficients of this decomposition are determined by the solutions of parabolic problems with one and two boundaries.

Article (Russian)

Complete asymptotic decomposition of the sojourn probability of a diffusion process in thin domains with moving boundaries

Gasanenko V. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 9. - pp. 1155–1164

We investigate a diffusion process ξ(t) with absorption defined in a thin domainD ε ={(x,t)∶εG 1 (t) 2 (t), t≥0}. We obtain the complete decomposition of the sojourn probability of ξ(t) inD ε with respect to ε→0.

Brief Communications (Ukrainian)

On certain exact relations for sojourn probabilities of a wiener process

Gasanenko V. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 6. - pp. 842–846

New exact relations are proved for the sojourn probability of a Wiener process between two time-de-pendent boundaries. The proof is based on the investigation of the heat-conduction equation in the domain determined by these functions-boundaries. The relations are given in the form of series.

Article (Ukrainian)

A limit theorem for mixing processes subject to rarefaction. II

Gasanenko V. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 5. - pp. 603–612

The limit theorem proved in the first part of this paper is applied to the well-known schemes of processes subject to rarefaction arising in queuing theory, mathematical biology, and in problems for counters.

Article (Ukrainian)

A limit theorem for mixing processes subject to rarefaction. I

Gasanenko V. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 4. - pp. 471–475

We prove a limit theorem on the approximation of point mixing processes subject to rarefaction by general renewal processes. This theorem contains a weaker condition on the mixing coefficient than the known conditions.

Article (Ukrainian)

Viability of solutions of many-dimensional stochastic differential equations

Gasanenko V. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 10. - pp. 1316–1323

We establish necessary and sufficient conditions for a many-dimensional diffusion process to reside in a fixed domain with probability one.

Article (Ukrainian)

Probability for a Wiener process to reside in tube domains for a long period of time

Gasanenko V. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 7. - pp. 912–917

We give various representations of asymptotics for the probability for a Wiener process to reside within a curvilinear strip during extended time intervals.

Article (Ukrainian)

Small deviations of solutions of stochastic differential equations in tube domains

Gasanenko V. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 5. - pp. 638–650

We present an algorithm for the determination of a complete asymptotic decomposition of the sojourn probability of a one-dimensional diffusion process in a thin domain with curvilinear boundary.

Article (Ukrainian)

A Wiener process in a curvilinear strip

Gasanenko V. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1990. - 42, № 4. - pp. 561–563

Article (Ukrainian)

Wiener process in a thin domain

Gasanenko V. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1988. - 40, № 2. - pp. 225-229

Article (Ukrainian)

Processes subject to rarefaction

Gasanenko V. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1983. - 35, № 1. - pp. 27—30