Asymptotic Methods in Probability and Statistics with Applications

Traditions of the 150-year-old St. Petersburg School of Probability and Statis­ tics had been developed by many prominent scientists including P. L. Cheby­ chev, A. M. Lyapunov, A. A. Markov, S. N. Bernstein, and Yu. V. Linnik. In 1948, the Chair of Probability and Statistics was established at the Department of Mathematics and Mechanics of the St. Petersburg State University with Yu. V. Linik being its founder and also the first Chair. Nowadays, alumni of this Chair are spread around Russia, Lithuania, France, Germany, Sweden, China, the United States, and Canada. The fiftieth anniversary of this Chair was celebrated by an International Conference, which was held in St. Petersburg from June 24-28, 1998. More than 125 probabilists and statisticians from 18 countries (Azerbaijan, Canada, Finland, France, Germany, Hungary, Israel, Italy, Lithuania, The Netherlands, Norway, Poland, Russia, Taiwan, Turkey, Ukraine, Uzbekistan, and the United States) participated in this International Conference in order to discuss the current state and perspectives of Probability and Mathematical Statistics. The conference was organized jointly by St. Petersburg State University, St. Petersburg branch of Mathematical Institute, and the Euler Institute, and was partially sponsored by the Russian Foundation of Basic Researches. The main theme of the Conference was chosen in the tradition of the St.

Contenu

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 Stochastic Differential Equations With Driving L2-Valued Measures Tightness of Stochastic 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