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Packing measure functions of subordinators sample paths

Authors:

Jinghai Feng Zhen Sha

Affiliation:

(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), andX[0,1]={xϕR:X(t)=x} for sometϕ[0,1]{. If φ(s)(sϕ(0,1)) is a measure function andh $(s) = left( {frac{{phi (s)}}{{gleft( {frac{1}{s}} right)}}} right)$ , then

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

. 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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