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Discrete Spaces of Elementary Events Read chapter Read first chapter

2013 | OriginalPaper | Chapter

11. Properties of the Trajectories of Random Walks. Zero-One Laws

Author : Alexandr A. Borovkov

Published in: Probability Theory

Publisher: Springer London

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Abstract

The chapter begins with Sect. 11.1 establishing the Borel–Cantelli and Kolmogorov zero-one laws, and also the zero-one law for exchangeable sequences. The concepts of lower and upper functions are introduced. Section 11.2 contains the first Kolmogorov inequality and several theorems on convergence of random series. Section 11.3 presents Kolmogorov’s Strong Law of Large Numbers and Wald’s identity for stopping times. Sections 11.4 and 11.5 are devoted to the Strong Law of Large Numbers for independent non-identically distributed random variables, and to the Strong Law of Large Numbers for generalised renewal processes, respectively.

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previous chapter Renewal Processes
next chapter Random Walks and Factorisation Identities
Footnotes
1
For more detail, see e.g. [31].
 
Literature
31.
Shiryaev, A.N.: Probability. Springer, New York (1984)
Metadata
Title
Properties of the Trajectories of Random Walks. Zero-One Laws
Author
Alexandr A. Borovkov
Copyright Year
2013
Publisher
Springer London
Book
Probability Theory

Print ISBN: 978-1-4471-5200-2

Electronic ISBN: 978-1-4471-5201-9

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-1-4471-5201-9_11