# Lacunary Series and Stable Distributions

Ontology type: schema:Chapter      Open Access: True

### Chapter Info

DATE

2015-04-08

AUTHORS ABSTRACT

By well-known results of probability theory, any sequence of random variables with bounded second moments has a subsequence satisfying the central limit theorem and the law of the iterated logarithm in a randomized form. In this paper we give criteria for a sequence (Xn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(X_n)$$\end{document} of random variables to have a subsequence (Xnk)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(X_{n_k})$$\end{document} whose weighted partial sums, suitably normalized, converge weakly to a symmetric stable distribution with parameter 0<α<2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0<\alpha <2$$\end{document}. More... »

PAGES

7-19

### Book

TITLE

Mathematical Statistics and Limit Theorems

ISBN

978-3-319-12441-4
978-3-319-12442-1

### Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-319-12442-1_2

DOI

http://dx.doi.org/10.1007/978-3-319-12442-1_2

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1047898206

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