The Packing Measure of the Trajectory of a One-Dimensional Symmetric Cauchy Process

A. C. Okoroafor

International Journal of Stochastic Analysis, 2008, vol. 2008, 1-7

Abstract:

Let ð ‘‹ ð ‘¡ = { ð ‘‹ ( ð ‘¡ ) , ð ‘¡ ≥ 0 } be a one-dimensional symmetric Cauchy process. We prove that, for any measure function, 𠜑 , 𠜑 − ð ‘ ( ð ‘‹ [ 0 , ð œ ] ) is zero or infinite, where 𠜑 − ð ‘ ( ð ¸ ) is the 𠜑 -packing measure of ð ¸ , thus solving a problem posed by Rezakhanlou and Taylor in 1988.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:564601

DOI: 10.1155/2008/564601

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