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Packing measure functions of subordinators sample paths

Authors:

Jinghai Feng Zhen Sha

Institution:

(1) Zhejiang University, 571#, 310027 Hangzhou, China

Abstract:

X(t) (t∉0,∞)) is a subordinator with its upper index β less than one, g(u) is the index function ofX(t), andX(t), andX0,1]={xϕR:X(t)=x} for sometϕ0,1]{. If φ(s)(sϕ(0,1)) is a measure function andh $(s) = \left( {\frac{{\phi (s)}}{{g\left( {\frac{1}{s}} \right)}}} \right)$ , then

$h - p(X0,1]) = \left\{ {\begin{array}{*{20}c} {0 a.s} \\ { + \infty a.s} \\ \end{array} } \right.according as \int_0^1 {\frac{{\varphi ^2 (s)}}{s}} ds \left\{ {\begin{array}{*{20}c} {< + \infty ,} \\ { = + \infty .} \\ \end{array} } \right.$

. The packing dimension ofX (t) is the uppcr index β. Project supported by the Natural Science Foundation of Zhejiang Province.

Keywords:

subordinator packing dimension measure function

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