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On the norm continuity of -valued Gaussian processes

Published online by Cambridge University Press:  22 January 2016

Itaru Mitoma
Affiliation:
Department of Mathematics, Kyushu University
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Extract

Let be the Schwartz space of all rapidly decreasing functions on Rn , be the topological dual space of and for each positive integer p, be the space of all elements of which are continuous in the p-th norm defining the nuclear Fréchet topology of . The main purpose of the present paper is to show that if {Xt, t ∈ [0, + ∞]} is an -valued Gaussian process and for any fixed φ ∈ the real Gaussian process {Xt(φ), t ∈ [0, + ∞)} has a continuous version, then for any fixed T > 0 there is a positive integer p such that {Xt, t ∈ [0, T]} has a version which is continuous in the norm topology of .

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1981

References

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