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Conditional Local Nondeterminism and Hausdorff Measure of Level Sets

Published online by Cambridge University Press:  20 November 2018

Narn-Rueih Shieh
Narn-Rueih Shieh*
Affiliation:
Department of Mathematics, National Taiwan University, Taipei, Taiwan
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Abstract

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Let X be a real stochastic process. We localize S. M. Berman's formulation on the local nondeterminism of X to a fixed level. With this localized idea, we prove that, for large classes of Gaussian and Markov X, at each x the level set X(t, w) = x has infinite Hausdorff ϕ - measure (ϕ is certain measure function) for w in a set of positive probability.

Keywords

60G17.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 1 , 01 March 1991 , pp. 123 - 127
Copyright
Copyright © Canadian Mathematical Society 1991

References

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