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Stable Convergence and Stable Limit Theorems

Weak convergence of probability measures or, what is the same, convergence in
distribution of random variables is arguably one of the most important basic concepts of asymptotic probability theory and mathematical statistics. The classical
central limit theorem for sums of independent real random variables, a cornerstone
of these fields, cannot possibly be thought of properly without the notion of weak
convergence/convergence in distribution. Interestingly, this limit theorem as well as
many others which are usually stated in terms of convergence in distribution remain
true under unchanged assumptions for a stronger type of convergence. This type of
convergence, called stable convergence with mixing convergence as a special case,
originates from the work of Alfred Rényi more than 50 years ago and has been used
by researchers in asymptotic probability theory and mathematical statistics ever
since (and should not be mistaken for weak convergence to a stable limit distribution). What seems to be missing from the literature is a single comprehensive
account of the theory and its consequences in applications, illustrated by a number
of typical examples and applied to a variety of limit theorems. The goal of this book
is to present such an account of stable convergence which can serve as an introduction to the area but does not compromise on mathematical depth and rigour.

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Detail Information
Series Title
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Call Number
-
Publisher
London : Springer.,
Collation
-
Language
English
ISBN/ISSN
978-3-319-18329-9
Classification
NONE
Content Type
text
Media Type
computer
Carrier Type
online resource
Edition
-
Subject(s)
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Specific Detail Info
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Statement of Responsibility
Other Information
Cataloger
Jemadi
Source
https://link.springer.com/content/pdf/10.1007/978-3-319-18329-9.pdf?pdf=button
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