Asymptotic Methods in Probability and Statistics with Applications

I: Probability Distributions.- 1 Positive Linnik and Discrete Linnik Distributions.- 2 On Finite—Dimensional Archimedean Copulas.- II: Characterizations of Distributions.- 3 Characterization and Stability Problems for Finite Quadratic Forms.- 4 A Characterization of Gaussian Distributions by Signs of Even Cumulants.- 5 On a Class of Pseudo-Isotropic Distributions.- III: Probabilities and Measures in High-Dimensional Structures.- 6 Time Reversal of Diffusion Processes in Hilbert Spaces and Manifolds.- 7 Localization of Marjorizing Measures.- 8 Multidimensional Hungarian Construction for Vectors with Almost Gaussian Smooth Distributions.- 9 On the Existence of Weak Solutions for Stochastic Differential Equations With DrivingL2-Valued Measures.- 10 Tightness of Stochastic Families Arising From Randomization Procedures.- 11 Long-Time Behavior of Multi-Particle Markovian Models.- 12 Applications of Infinite-Dimensional Gaussian Integrals.- 13 On Maximum of Gaussian Non-Centered Fields Indexed on Smooth Manifolds.- 14 Typical Distributions: Infinite-Dimensional Approaches.- IV: Weak and Strong Limit Theorems.- 15 A Local Limit Theorem for Stationary Processes in the Domain of Attraction of a Normal Distribution.- 16 On the Maximal Excursion Over Increasing Runs.- 17 Almost Sure Behaviour of Partial Maxima Sequences of Somem-Dependent Stationary Sequences.- 18 On a Strong Limit Theorem for Sums of Independent Random Variables.- V: Large Deviation Probabilities.- 19 Development of Linnik’s Work in His Investigation of the Probabilities of Large Deviation.- 20 Lower Bounds on Large Deviation Probabilities for Sums of Independent Random Variables.- VI: Empirical Processes, Order Statistics, and Records.- 21 Characterization of Geometric Distribution Through Weak Records.- 22Asymptotic Distributions of Statistics Based on Order Statistics and Record Values and Invariant Confidence Intervals.- 23 Record Values in Archimedean Copula Processes.- 24 Functional CLT and LIL for Induced Order Statistics.- 25 Notes on the KMT Brownian Bridge Approximation to the Uniform Empirical Process.- 26 Inter-Record Times in Poisson PacedF?Models.- VII: Estimation of Parameters and Hypotheses Testing.- 27 Goodness-of-Fit Tests for the Generalized Additive Risk Models.- 28 The Combination of the Sign and Wilcoxon Tests for Symmetry and Their Pitman Efficiency.- 29 Exponential Approximation of Statistical Experiments.- 30 The Asymptotic Distribution of a Sequential Estimator for the Parameter in an AR(1) Model with Stable Errors.- 31 Estimation Based on the Empirical Characteristic Function.- 32 Asymptotic Behavior of Approximate Entropy.- VIII: Random Walks.- 33 Threshold Phenomena in Random Walks.- 34 Identifying a Finite Graph by Its Random Walk.- IX: Miscellanea.- 35 The Comparison of the Edgeworth and Bergström Expansions.- 36 Recent Progress in Probabilistic Number Theory.- X: Applications to Finance.- 37 On Mean Value of Profit for Option Holder: Cases of a Non-Classical and the Classical Market Models.- 38 On the Probability Models to Control the Investor Portfolio.