Proceedings of the Bakuriani Colloquium in Honour of Yu.V. Prohorov, Bakuriani, Georgia, USSR, 24 February–4 March, 1990

Abstract

Part 1 Limit theorems - finite-dimensional case: on the bounds for the probabilities of large deviations for random variables and vectors, Sh.S. Ebralidze the influence of extreme summands on the law of iterated logarithm, M.U. Gafurov and I.M. Hamdamov generalized Marcinkiewicz's theorem and asymptotic expansions in the central limit theorem, L.B. Klebanov and J.A. Melamed on integrability of sup [Snk/nk], O.I. Klesov asymptotic expansions in large deviation zones for the distribution density of sums of independent random variables, L. Saulis strong law of large numbers for operator normalized sums of independent random vectors, S. Solntsev. Part 2 Limit theorems in general spaces: on the distribution of the sup-norm for a stable motion and the rate of convergence, M. Bloznelis semi-invariant conditions of weak convergence of random processes in the space of continuous functions, V. Buldygin almost sure permutational convergence of vector random series and Kolmogorov's problem. S.A. Chobanyan and G.J. Giorgobiani limit theorems for stable laws in Banach spaces, A.N. Chupronov an estimate of the rate of convergence in the CLT for dependent Hilbert space valued random variables, P. Gudynas an improved estimate of the accuracy of Gaussian approximation in Hilbert space, V.V. Sazonov and V.V. Ulyanov on large deviations for L-estimates, R. Zitkis. Part 3 Limit theorems for stochastic processes: rates of convergence in the invariance principle for empirical processes, V.I. Kolchinskii ergodic theorem for semimartingale-helix, R. Sh. Liptser ergodic theorems for discrete time random processes, S.V. Nagaev on functional principle of large deviations, A. Puhalskii. Part 4 Probabilities in general spaces: some properties of Gaussian measures and potentials in Martingale spaces with mixed norm, A.D. Bendikov unexpected limit behaviour of the Gaussian tail probabilities, M.A. Lifshits topologies on the space of sigma-additive cylindrical probabilities, D.H. Mushtari two-sided exponential inequalities for the distribution of the norm of Banach space valued random variables, E.J. Ostrovskii nonuniform estimates of the density of the squared norm of a Gaussian vector in Hilbert space, V.V. Ulyanov on sequential conditions for a cylindrical measure to be countably additive, Yu. N. Vladimirskii a family of measures admitting consistent estimates, Z.S. Zerakidze. Part 5 Stochastic analysis and control. Part 6 Mathematical statistics. Part 7 Towards natural sciences: on condensable point processes, R.V. Ambartzumian the ground state of a random stationary medium in the mean field approximation, A. Astrauskas and S.A. Molchanov scaling behaviour of random walks with topological constraints, S.K. Nechaev and Ya.G. Sinai covergence of the stochastic quantization method for lattice R-gauge theories, V. Sidoravicius.