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Everywhere irregularity of certain classes of random processes with stationary Gaussian increments

Published online by Cambridge University Press:  01 July 2016

P. L. Davies
P. L. Davies*
Affiliation:
University of Konstanz
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Abstract

This paper is concerned with everywhere local behaviour of certain classes of random processes which have stationary Gaussian increments. It is shown that for two classes of processes almost all the sample functions have the following property. The supremum of the increments in the neighbourhood of a point is everywhere of larger order than the standard deviation. For a third class of processes it is shown that the supremum is at least of the same order as the standard deviation.

Keywords

GAUSSIAN PROCESSESSTATIONARY INCREMENTSEVERYWHERE IRREGULARITYSUPREMUM OF INCREMENTS

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 5 , Issue 1 , April 1973 , pp. 103 - 118
Copyright
Copyright © Applied Probability Trust 1973 

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