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Multiple images of stochastic processes

Published online by Cambridge University Press:  24 October 2008

Simeon M. Berman
Simeon M. Berman
Affiliation:
Courant Institute of Mathematical Sciences, New York University
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Abstract

A simple sufficient condition is given for a stochastic process x(t), 0 ≤ t ≤ 1, to have the following property: There is an integer m ≥ 2 such that for any non-degenerate subinterval J ⊂ [0, 1], there exist m disjoint subintervals I1, …, Im ⊂ J such that the intersection of the images of I1,…, Im under the mapping by x(·) has positive Lebesgue measure, almost surely. There is also a version for vector random fields; and the main result is shown to apply to large classes of processes.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 94 , Issue 1 , July 1983 , pp. 183 - 188
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

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