Theory of Stochastic Processes, 2007 (Volume 13 (29)) http://dspace.nbuv.gov.ua:80/handle/123456789/3051 2026-04-05T17:46:05Z 2026-04-05T17:46:05Z Long-term returns in stochastic interest rate models Zubchenko, V. http://dspace.nbuv.gov.ua:80/handle/123456789/4528 2009-11-25T10:00:39Z 2007-01-01T00:00:00Z Long-term returns in stochastic interest rate models Zubchenko, V. We consider the behavior of integral functional of the solution of stochastic differential equation with coefficients contained small parameter. The dependence on the order of small parameter in every term of equation with Wiener process and Poisson measure term is studied. We observe the convergence of the long-term return, using an extension of the Cox-Ingersoll-Ross stochastic model of the short interest rate. Obtained results are applied for studying of two-factor stochastic interest rate model. 2007-01-01T00:00:00Z Strong invariance principle for renewal and randomly stopped processes Zinchenko, N. http://dspace.nbuv.gov.ua:80/handle/123456789/4527 2009-11-25T10:00:32Z 2007-01-01T00:00:00Z Strong invariance principle for renewal and randomly stopped processes Zinchenko, N. The strong invariance principle for renewal process and randomly stopped sums when summands belong to the domain of attraction of an α-stable law is presented 2007-01-01T00:00:00Z Random process from the class V(φ,ψ): exceeding a curve Yamnenko, R. Vasylyk, O. http://dspace.nbuv.gov.ua:80/handle/123456789/4526 2010-03-01T15:26:32Z 2007-01-01T00:00:00Z Random process from the class V(φ,ψ): exceeding a curve Yamnenko, R.; Vasylyk, O. Random processes from the class V (φ, ψ) which is more general than the class of ψ-sub-Gaussian random process. The upper estimate of the probability that a random process from the class V (φ, ψ) exceeds some function is obtained. The results are applied to generalized process of fractional Brownian motion. 2007-01-01T00:00:00Z Stationary processes in functional spaces Lq( R ) Yakovenko, T. http://dspace.nbuv.gov.ua:80/handle/123456789/4525 2009-11-25T10:00:39Z 2007-01-01T00:00:00Z Stationary processes in functional spaces Lq( R ) Yakovenko, T. The paper is devoted to the problem of establishing the conditions on the stochastic process to belong it to the functional space Lq(R) with probability one. The corresponding results were obtained for the strictly Orlicz, stationary in wide sense processes. 2007-01-01T00:00:00Z