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Conditional Local Nondeterminism and Hausdorff Measure of Level Sets
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
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- Copyright © Canadian Mathematical Society 1991