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Fonctions Certaines Admettant des Répartitions Asymptotiques et Fonctions Aléatoires Stationnaires

Published online by Cambridge University Press:  05 September 2017

A. Blanc-Lapierre
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Abstract

In the article below, we consider sets of non-random functions of time t admitting certain asymptotic distributions. Purely temporal and deterministic considerations lead us to associate to a set , say, of functions H(t) of this type, a space Ω of samples ω.

To each function H(t) ⊂ , there corresponds a random variable h (ω). To the set of translated functions H(t + λ) of a function H(t) ⊂ , there corresponds a stationary random function of the translation parameter λ, say, h(λ, ω). We study the transposition to the set of non-random functions H(t) of such properties as moments, gaussian character, independence, harmonic analysis, and others, of the random variables h (ω) and of the random functions h (λ, ω).

Some remarks are made concerning the links between ergodicity and the above problems.

Type
Part V — Stochastic Processes
Information
Journal of Applied Probability , Volume 12 , Issue S1 , 1975 , pp. 177 - 185
Copyright
Copyright © 1975 Applied Probability Trust 

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References

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