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

V. V. Sazonov, T. Shervashidze, V. V. Sazonov, T. Shervashidze

• Publisher: De Gruyter
• Year: 2020
• Print ISBN:
  9783112302484
• eBook ISBN:
  9783112313626
• Topic: Mathematics
• Subtopic: Algebra
• Index: Mathematics

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Table of contents

• 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 [S_nk/n_k]
• 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