New Trends in Probability and Statistics. Vol. 1 Proceedings of the Bakuriani Colloquium in Honour of Yu.V. Prohorov, Bakuriani, Georgia, USSR, 24 February{u2013}4 March, 1990

Cellulose nanocrystals are being used more frequently as processing and nanofabrication techniques have advanced considerably. Cellulose Nanocrystals includes topics including Extraction and Fabrication Methodologies, Scale-Up Strategies and Life Cycle Assessment, Surface Modification Strategies, Nanocomposites, and Characterization and Testing Protocols. This book will appeal to physical, chemical and biological scientists as well as engineers. 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