New Trends in Probability and Statistics. / Vol. 1, : Proceedings of the Bakuriani Colloquium in Honour of Yu.V. Prohorov, Bakuriani, Georgia, USSR, 24 February–4 March, 1990 / / ed. by T. Shervashidze, V. V. Sazonov.

• Superior document: Title is part of eBook package: De Gruyter DGBA Mathematics - 1990 - 1999
• MitwirkendeR: Ambartzumian, R. V.,; Astrauskas, A.,; Bendikov, A. D.,; Bloznelis, M.,; Buldygin, V.,; Chibisov, D. M.,; Chitashvili, R. J.,; Chobanyan, S. A.,; Chuprunov, A. N.,; Dorogovtsev, A. Ya.,; Ebralidze, Sh. S.,; Evstigneev, I. V.,; Gafurov, M. U.,; Giorgobiani, G. J.,; Glonti, O. A.,; Gudynas, P.,; Hamdamov, I. M.,; Jamburia, L. G.,; Kabanov, Yu. M.,; Katyshev, P. K.,; Khokhlov, V. J.,; Klebanov, L. B.,; Klesov, O. I.,; Kolchin, V. F.,; Kolchinskii, V. I.,; Koval, V.,; Lazrieva, N. L.,; Lifshits, M. A.,; Liptser, R. Sh.,; Lugavov, V. S.,; Makhno, S.,; Mania, M. G.,; Melamed, J. A.,; Mishura, Yu. S.,; Mnatsakanov, R. M.,; Molchanov, S. A.,; Mushtari, D. H.,; Nagaev, A. V.,; Nagaev, S. V.,; Nazin, A. V.,; Nechaev, S. K.,; Ostrovskii, E. I.,; Pergamenshchikov, S. M.,; Puhalskii, A.,; Purtukhia, O.,; Radavlcius, M.,; Rogozin, B. A.,; Rotar, V. I.,; Sauiis, L.,; Sazonov, V. V.,; Shemyakin, A. E.,; Sidoravicius, V.,; Sinai, Ya. G.,; Sokhadze, G.,; Solntsev, S.,; Stoyanov, J. M.,; Toronjadze, T. A.,; Tsertsvadze, K. A.,; Ulyanov, V. V.,; Vladimirskii, Yu. N.,; Zerakidze, Z. S.,; Zitikis, R.,
• HerausgeberIn: Sazonov, V. V.,; Shervashidze, T.,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2020]; ©1991
• Year of Publication: 2020
• Edition: Reprint 2020
• Language: English
• Series: New Trends in Probability and Statistics ; Vol. 1
• Physical Description: 1 online resource (IX, 702 p.) :; 1 frontisp., num. figs

Table of Contents

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 of a Random Stationary Medium in the Mean Field Approximation -- Scaling Behavior of Random Walks with Topological Constraints -- Convergence of the Stochastic Quantization Method for Lattice R-Gauge Theories -- List of Contributors -- Organizing Committee and Acknowledgement