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Asymptotic Methods in Probability and Statistics with Applications

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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.

Author(s): Gerd Christoph, Karina Schreiber (auth.), N. Balakrishnan, I. A. Ibragimov, V. B. Nevzorov (eds.)
Series: Statistics for Industry and Technology
Edition: 1
Publisher: Birkhäuser Basel
Year: 2001

Language: English
Pages: 549
Tags: Operations Research, Management Science; Statistical Theory and Methods

Front Matter....Pages i-xxiii
Front Matter....Pages 1-1
Positive Linnik and Discrete Linnik Distributions....Pages 3-17
On Finite-Dimensional Archimedean Copulas....Pages 19-35
Front Matter....Pages 37-37
Characterization and Stability Problems for Finite Quadratic Forms....Pages 39-50
A Characterization of Gaussian Distributions by Signs of Even Cumulants....Pages 51-54
On a Class of Pseudo-Isotropic Distributions....Pages 55-62
Front Matter....Pages 63-63
Time Reversal of Diffusion Processes in Hilbert Spaces and Manifolds....Pages 65-79
Localization of Majorizing Measures....Pages 81-100
Multidimensional Hungarian Construction for Vectors With Almost Gaussian Smooth Distributions....Pages 101-132
On the Existence of Weak Solutions for Stochastic Differential Equations With Driving L 2 -Valued Measures....Pages 133-142
Tightness of Stochastic Families Arising From Randomization Procedures....Pages 143-159
Long-Time Behavior of Multi-Particle Markovian Models....Pages 161-176
Applications of Infinite-Dimensional Gaussian Integrals....Pages 177-187
On Maximum of Gaussian Non-Centered Fields Indexed on Smooth Manifolds....Pages 189-203
Typical Distributions: Infinite-Dimensional Approaches....Pages 205-212
Front Matter....Pages 213-213
A Local Limit Theorem for Stationary Processes in the Domain of Attraction of a Normal Distribution....Pages 215-223
On the Maximal Excursion Over Increasing Runs....Pages 225-242
Almost Sure Behaviour of Partial Maxima Sequences of Some m -Dependent Stationary Sequences....Pages 243-249
On a Strong Limit Theorem for Sums of Independent Random Variables....Pages 251-256
Front Matter....Pages 257-257
Development of Linnik’s Work in His Investigation of the Probabilities of Large Deviation....Pages 259-275
Lower Bounds on Large Deviation Probabilities for Sums of Independent Random Variables....Pages 277-295
Front Matter....Pages 297-297
Characterization of Geometric Distribution Through Weak Records....Pages 299-307
Asymptotic Distributions of Statistics Based on Order Statistics and Record Values and Invariant Confidence Intervals....Pages 309-320
Record Values in Archimedean Copula Processes....Pages 321-331
Functional CLT and LIL for Induced Order Statistics....Pages 333-349
Notes on the KMT Brownian Bridge Approximation to the Uniform Empirical Process....Pages 351-369
Inter-Record Times in Poisson Paced F α Models....Pages 371-382
Front Matter....Pages 383-383
Goodness-of-Fit Tests for the Generalized Additive Risk Models....Pages 385-394
The Combination of the Sign and Wilcoxon Tests for Symmetry and Their Pitman Efficiency....Pages 395-407
Exponential Approximation of Statistical Experiments....Pages 409-423
The Asymptotic Distribution of a Sequential Estimator for the Parameter in an AR(1) Model With Stable Errors....Pages 425-434
Estimation Based on the Empirical Characteristic Function....Pages 435-449
Asymptotic Behavior of Approximate Entropy....Pages 451-461
Front Matter....Pages 463-463
Threshold Phenomena in Random Walks....Pages 465-485
Identifying a Finite Graph by Its Random Walk....Pages 487-490
Front Matter....Pages 491-491
The Comparison of the Edgeworth and Bergström Expansions....Pages 493-506
Recent Progress in Probabilistic Number Theory....Pages 507-519
Front Matter....Pages 521-521
On Mean Value of Profit for Option Holder: Cases of a Non-Classical and the Classical Market Models....Pages 523-533
On the Probability Models to Control the Investor Portfolio....Pages 535-546
Back Matter....Pages 547-549