Theory of Stochastic Processes, 2007, № 4 http://dspace.nbuv.gov.ua:80/handle/123456789/3054 Sun, 05 Apr 2026 17:40:17 GMT 2026-04-05T17:40:17Z Theory of Stochastic Processes, 2007, № 4 http://dspace.nbuv.gov.ua:80/bitstream/id/168105/ http://dspace.nbuv.gov.ua:80/handle/123456789/3054 Long-term returns in stochastic interest rate models http://dspace.nbuv.gov.ua:80/handle/123456789/4528 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. Mon, 01 Jan 2007 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/4528 2007-01-01T00:00:00Z Strong invariance principle for renewal and randomly stopped processes http://dspace.nbuv.gov.ua:80/handle/123456789/4527 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 Mon, 01 Jan 2007 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/4527 2007-01-01T00:00:00Z Random process from the class V(φ,ψ): exceeding a curve http://dspace.nbuv.gov.ua:80/handle/123456789/4526 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. Mon, 01 Jan 2007 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/4526 2007-01-01T00:00:00Z Stationary processes in functional spaces Lq( R ) http://dspace.nbuv.gov.ua:80/handle/123456789/4525 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. Mon, 01 Jan 2007 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/4525 2007-01-01T00:00:00Z