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

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  • A. C. Okoroafor

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.

Suggested Citation

  • A. C. Okoroafor, 2008. "The Packing Measure of the Trajectory of a One-Dimensional Symmetric Cauchy Process," International Journal of Stochastic Analysis, Hindawi, vol. 2008, pages 1-7, September.
    • Handle: RePEc:hin:jnijsa:564601
    DOI: 10.1155/2008/564601
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