Proceedings of the Bakuriani Colloquium in Honour of Yu.V. Prohorov, Bakuriani, Georgia, USSR, 24 February4 March, 1990

Frontmatter -- CONTENTS -- Preface -- Bakuriani Colloquia on Probability Theory and Mathematical Statistics -- I. LIMIT THEOREMS: FINITE - DIMENSIONAL CASE -- On the Bounds for the Probabilities of Large Deviations for Random Variables and Vectors -- The Influence of Extremes Summands on the Law of Iterated Logarithm -- Generalized Marcinkiewicz's Theorem and Asymptotic Expansions in the Central Limit Theorem -- On Integrability of sup [Snk /nk] -- Asymptotic Expansions in Large Deviation Zones for the Distribution Density of Sums of Independent Random Variables -- Strong Law of Large Numbers for Operator Normalized Sums of Independent Random Vectors -- II. LIMIT THEOREMS IN GENERAL SPACES -- On the Distribution of the Sup-Norm for a Stable Motion and the Rate of Convergence -- Semi-Invariant Conditions of Weak Convergence of Random Processes in the Space of Continuous Functions -- Almost Sure Permutational Convergence of Vector Random Series and Kolmogorov's Problem -- Limit Theorems for Stable Laws in Banach Spaces -- An Estimate of the Rate of Convergence in the CLT for Dependent Hilbert Space Valued Random Variables -- An Improved Estimate of the Accuracy of Gaussian Approximation in Hilbert Space -- On Laxge Deviations for L-Estimates -- III. LIMIT THEOREMS FOR STOCHASTIC PROCESSES -- Rates of Convergence in the Invariance Principle for Empirical Processes -- Ergodic Theorem for Semimartingale-Helix -- Ergodic Theorems for Discrete Time Random Processes -- On Functional Principle of Large Deviations -- IV. PROBABILITIES IN GENERAL SPACES -- Some Properties of Gaussian Measures and Potentials in Martingale Spaces with Mixed Norm -- Unexpected Limit Behaviour of the Gaussian Tail Probabilities -- Topologies on the Space of a-Additive Cylindrical Probabilities -- Two-Sided Exponential Inequalities for the Distribution of the Norm of Banach Space Valued Random Variables -- Nonuniform Estimates of the Density of the Squared Norm of a Gaussian Vector in Hilbert Space -- On Sequential Conditions for a Cylindrical Measure to be Countably Additive -- A Family of Measures Admitting Consistent Estimates -- V. STOCHASTIC ANALYSIS AND CONTROL -- Asymptotic Behaviour of Solutions of Stochastic Equations -- On the Decomposition of a Maximum of Semimartingales and Ito's Generalized Formula -- Optimal Transmission of Gaussian Signals Involving Cost for Transmission and Feedback -- Stationary and Periodic Solutions of Stochastic Difference and Differential Equations in Banach Space -- Controlled Random Fields on Graphs and Stochastic Models of Economic Equilibrium -- Asymptotic Expansions for Singulary Perturbed Stochastic Differential Equations -- On Uniformly Optimal Coding of Gaussian Messages in White Gaussian Channels with Feedback -- On the Structure of a Random Graph with Nonuniform Distribution -- Identities for Ladder Functionals of Homogeneous Random Processes and Walks with Independent Increments -- On Convergence of Solutions of Stochastic Equations -- Stochastic Integrals and Stochastic Differential Equations on the Plane Involving Strong Semimartingales -- Itó-Ventsel' Formula For Anticipative Processes -- Connectivity Property and Optimality Almost Surely and in Probability -- Absolute Continuity of Smooth Measures Generated by Nonlinear Equations -- VI. MATHEMATICAL STATISTICS -- A New Method of Asymptotic Analysis of Simple Linear Rank Statistics -- On Stable M-Estimators in the Partial Likelihood Scheme -- Asymptotic Estimation of Integrals of Certain Random Fields -- On Minimax Bound for Parameter Estimation in Ball (Bias Accounting) -- Limit Theorems for Some Random Processes Based on Frequencies -- From Asymptotic Efficiency in Minimax Sense to Bahadur Efficiency -- On Estimating Parameters of a Distribution Concentrated in a Circle -- On the Approximation of the Likelihood Function by a Vector Analogue of the Whittle Statistics -- VII. TOWARDS NATURAL SCIENCES -- On Condensable Point Processes -- The Ground State