Klebanov L.B. Heavy tailed distributions

Prague: Matfyzpress, 2003. — 208 p.Main examples of heavy tailed distributions
Pareto distribution
Strictly stable distributions
Random stability
Stable distributions
Definition of stable distributions
Existence of moments
The densities of stable distributions
Some series representations for stable random variables
Subgaussian distributions
Simulation
A linear method of statistical parameter estimation
Multivariate stable distributions
Stable random vectors
A counterexample for < α <
Characteristic function of an α-stable random vector
Sub-Gaussian vectors
Series representation in multidimensional case
ν-infinitely divisible and stable distributions
Sums of a random number of random variables
Some limit and transfer theorems
The definition and existence of a ν-Gaussian random variable
Examples of summation schemes admitting ν-strictly Gaussian laws
A generalization of the Marcinkiewicz theorem
ν-Infinitely divisible random variables
Accompanying laws
Approximations of random sums
Geometric stable distributions
A generalization of stable laws
New Representations for Multivariate Geo-stable Distributions
On the Reliability of Hierarchical Structures
Ill-posed problems
Main considerations
Introduction and motivating examples
Central Pre-Limit Theorem
Sums of a random number of random variables
Local pre-limit theorems and their applications to finance
Pre-limit theorem for extremums
Relations with robustness of statistical estimators
Statistical estimation for non-smooth densities
Entire functions of exponential type
Main definitions
Fourier transform of the functions from M ν,p
Interpolation formula
Inequality of different metrics
Valle’e Poussin kernels
Application to statistical density estimation
Generalized functions
Main definitions
Definition of Fourier transform for generalized functions
Functions φ ε and ψ εAuthor Index