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Oscillation Function of a Multiparameter Gaussian Process

Published online by Cambridge University Press:  22 January 2016

Naresh C. Jain  and
G. Kallianpur
Naresh C. Jain
Affiliation:
University of Minnesota
G. Kallianpur
Affiliation:
University of Minnesota
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Abstract

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It is our object in this paper to show that the recent results of K. Ito and M. Nisio [4] on the oscillation function of Gaussian processes on [0,1] are valid for Gaussian processes with a general multiparameter “time” set T. Except in extending Theorem 4 of [4] where we assume T to be the d-dimensional cube, in all other cases we allow T to be a separable metric space. Despite the generality of the time set, the proofs are achieved essentially using the method of the above mentioned authors. However, in Theorem 1 below we find the use of Lemma 6 of [5] more convenient than the approach via orthogonal expansions and Kolmogorov’s zero-one law as is done in [4].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 47 , September 1972 , pp. 15 - 28
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1972

References

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