On limit distributions of the time of first passage over a high level

On limit distributions of the time of first passage over a high level We describe a simple method of finding the limit distribution of the time of first passage over a high level for a random sequence (or random process). The method reduces the considered problem to a well-studied problem of finding the distribution of this random sequence (or process) at a certain fixed time. This allows to consider not only traditional sums of independent random variables but also sums of dependent random variables. As examples, sums of independent random variables with stable limit distribution functions, sequential testing of hypotheses, and problems of the first passage over a high level for Gaussian processes with strong dependencies are considered. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

On limit distributions of the time of first passage over a high level

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Publisher
Pleiades Publishing
Copyright
Copyright © 2015 by Pleiades Publishing, Inc.
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S0032946015020064
Publisher site
See Article on Publisher Site

Abstract

We describe a simple method of finding the limit distribution of the time of first passage over a high level for a random sequence (or random process). The method reduces the considered problem to a well-studied problem of finding the distribution of this random sequence (or process) at a certain fixed time. This allows to consider not only traditional sums of independent random variables but also sums of dependent random variables. As examples, sums of independent random variables with stable limit distribution functions, sequential testing of hypotheses, and problems of the first passage over a high level for Gaussian processes with strong dependencies are considered.

Journal

Problems of Information TransmissionSpringer Journals

Published: Jul 7, 2015

References

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