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Weak Convergence of the Row Sums of a Triangular Array of Empirical Processes Read chapter Read first chapter

1998 | OriginalPaper | Chapter

Oscillations of Gaussian Stein’s Elements

Authors : Mikhail Lifshits, Michel Weber

Published in: High Dimensional Probability

Publisher: Birkhäuser Basel

Included in: Professional Book Archive

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In this paper we investigate the properties of a remarkable class of Gaussian sequences arising from E.M. Stein’s probabilistic approach to continuity principle in ergodic theory followed by spectacular applications in real analysis due to J. Bourgain and further investigations of the second named author. For such sequences, we obtain a nearly complete picture of the properties of the oscillations and describe the weak and strong convergence properties of associated sojourn times.

previous chapter A Central Limit Theorem for the Sock-Sorting Problem
next chapter A Sufficient Condition for the Continuity of High Order Gaussian Chaos Processes
Metadata
Title
Oscillations of Gaussian Stein’s Elements
Authors
Mikhail Lifshits
Michel Weber
Copyright Year
1998
Publisher
Birkhäuser Basel
Book
High Dimensional Probability

Print ISBN: 978-3-0348-9790-7

Electronic ISBN: 978-3-0348-8829-5

Copyright Year: 1998

DOI
https://doi.org/10.1007/978-3-0348-8829-5_15