http://dspace.nbuv.gov.ua:80/handle/123456789/3053 2026-04-15T18:10:58Z http://dspace.nbuv.gov.ua:80/handle/123456789/4509 Homogeneous Markov chains in compact spaces Skorokhod, A.V. For homogeneous Markov chains in a compact and locally compact spaces, the ergodic properties are investigated, using the notions of topological recurrence and connections. 2007-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/4508 Local time as an element of the Sobolev space Rudenko, A.V. For a centered Gaussian random ?eld taking its values in R^d, we investigate the existence of a local time as a generalized functional, i.e an element of some Sobolev space. We give the sfficient condition for such an existence in terms of the field covariation and apply it in several examples: the self-intersection local time for a fractional Brownian motion and the intersection local time for two Brownian motions. 2007-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/4507 The decomposition of a solution of the quasilinear stochastic parabolic equation with weak source Melnik, S. We obtain conditions which guarantee the existence of a decomposition of a solution of the quasilinear stochastic parabolic equation with a weak source. 2007-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/4506 Local limit theorem for triangular array of random variables Korchinsky, I.A.; Kulik, A.M. For a triangular array of random variables {Xk,n, k = 1, . . . , cn; n belongs N} such that, for every n, the variables X1,n, . . .,Xcn,n are independent and identically distributed, the local limit theorem for the variables Sn = X1,n + · · · + Xcn,n is established. 2007-01-01T00:00:00Z