Perturbation of functions by the paths of a Lévy process
Published online by Cambridge University Press: 24 October 2008
Extract
In a recent paper Mountford [4] showed, using an ingenious probabilistic argument, that if X is a real-valued stable process with index α < 1 and f: [0, ∞) → ℝ is a non-constant continuous function, then
where we use the notation |A| for the Lebesgue measure of a Lebesgue measurable set A ⊂ ℝ. The argument in [4] appears to make strong use of the strict scaling properties of X and the ‘intermediate value’ property of f.
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- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 105 , Issue 2 , March 1989 , pp. 377 - 380
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- Copyright © Cambridge Philosophical Society 1989
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