http://dspace.nbuv.gov.ua:80/handle/123456789/3056 2026-04-05T16:17:10Z http://dspace.nbuv.gov.ua:80/handle/123456789/4451 Vertical and horizontal fluid queues in heavy and low traffic Zakusilo, O.K.; Lysak, N.P. The paper considers vertical and horizontal fluid queueing systems with consecutive service. The workload processes in these systems satisfy the Langevin equations with Poisson input. The objective is to investigate the main stationary characteristics in heavy and low traffic. 2006-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/4450 Matrix parameter estimation in an autoregression model Yurachkivsky, A.P.; Ivanenko, D.O. The vector difference equation ξk = Af(ξk−1)+εk, where (εk) is a square integrable difference martingale, is considered. A family of estimators ˇAn depending, besides the sample size n, on a bounded Lipschitz function is constructed. Convergence in distribution of √n (ˇAn − A) as n→∞is proved with the use of stochastic calculus. Ergodicity and even stationarity of (εk) is not assumed, so the limiting distribution may be, as the example shows, other than normal. 2006-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/4449 Existence of generalized local times for Gaussian random fields Rudenko, A. We consider a Gaussian centered random field that has values in the Euclidean space. We investigate the existence of local time for the random field as a generalized functional, an element of the Sobolev space constructed for our random field. We give the sufficient condition for such an existence in terms of the field covariation and apply it in a few examples: the Brownian motion with additional weight and the intersection local time of two Brownian motions. 2006-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/4448 Support theorem on stochastic flows with interaction Pilipenko, A.Yu. We prove an analogue of the Stroock–Varadhan theorem for stochastic flows describing a motion of interacting particles in a random media. A version of the Itˆo lemma for functions on a measure-valued process is obtained. 2006-01-01T00:00:00Z