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This book represents thirty-eight extensive and carefully edited chapters written by prominent researchers, providing an up-to-date survey of new asymptotic methods in science and technology. The chapters contain broad coverage of the latest developments and innovative techniques in a wide range of theoretical and numerical issues in the field of asymptotic methods in probability and mathematical statistics.
The book is organized into ten thematic parts: probability distributions; characterizations of distributions; probabilities and measures in high dimensional structures; weak and stron limit theorems; large deviation probabilities; empirical processes; order statistics and records; estimation of parameters and hypotheses testing; random walks, and applications to finance. Written in an accessible style, this book conveys a clear and practical perspective of asymptotic methods.
Topics and features:Recent developments in asymptotic methods;
Parametric and Nonparametric Inference; Distribution Theory;
Shastic Processes; Order Statistics; Record values and
Asymptotic methods in Probability and Mathematical Statistics is an essential resource for reseachers, practitioners, and professionals involved in Theoretical and Applied Probability and/or in Theoretical and Applied Statistics. Various chapters of the volume will also appeal to industrial statisticians and financial economists.
Preface Contributors Part I: Probability Distributions Positive Linnik and Discrete Linnik Distributions On Finite—Dimensional Archimedean Copulas Part II: Charazterizations of Distributions Characterization and Stability Problems for Finite Quadratic Forms A Characterization of Gaussian Distributions by Signs and Even Cumulants On a Class of Pseudo-Isotropic Distributions Part III: Probabilities and Measures in High-Dimensional Structures Time Reversal of Diffusion Processes in Hilbert Spaces and Manifolds Localization of Marjorizing Measures Multidimensional Hungarian Construction for Vectors with Almost Gaussian Smooth Distributions On the Existence of Weak Solutions for Shastic Differential Equations With Driving L2-Valued Measures Tightness of Shastic Families Arising From Randomization Procedures Long-Time Behavior of Multi-Particle Markovian Models Applications of Infinite-Dimensional Gaussian Integrals On Maximum of Gaussian Non-Centered Fields Indexed on Smooth Manifolds Typical Distributions: Infinite-Dimensional Approaches Part IV: Weak and Strong Limit Theorems A Local Limit Theorem for Stationary Processes in the Domain of Attraction of a Normal Distribution On the Maximal Excursion Over Increasing Runs Almost Sure Behaviour of Partial Maxima Sequences of Some m-Dependent Stationary Sequences On a Strong Limit Theorem for Sums of Independent Random Variables Part V: Large Deviation Probabilities Development of Linnik's Work in His Investigation of the Probabilities of Large Deviation Lower Bounds on Large Deviation Probabilities for Sums of Independent Random Variables Part VI: Empirical Processes, Order Statistics, and Records Characterization of Geometric Disribution Through Weak Records Asymptotic Distributions of Statistics Based on Order Statistics and Record Values and Invariant Confidence Intervals Record Values in Archimedean Copula Processes Functional CLT and LIL for Induced Order Statistics Notes on the KMT Brownian Bridge Approximation to the Uniform Empirical Process Inter-Record Times in Poisson paced Fa Models Part VII: Estimation of Parameters and Hypotheses Testing Goodness-of Fit Tests for the Generalized Additive Risk Models The Combination of the Sign and Wilcoxon Tests for Symmetry and Their Pitman Efficiency Exponential Approximation of Statistical Experiments The Asymptotic Distribution of a Sequential Estimator for the Paramater in an AR(1) Model with Stable Errors Estimation Based on the Empirical Characteristic Function Asymptotic Behavior of Approximate Entropy Part VIII: Random Walks Threshold Phenomena in Random Walks Identifying a Finite Graph by Its Random Walk Part IX: Miscellanea The Comparison of the Edgeworth and Bergström Expansions Recent Progress in Probabilistic Number Theory On Mean Value of Profit for Option Holder: Cases of a Non-Classical and the Classical Market Models On the Probability Models to Control the Investor Portfolio Index