Functional Central Limit Theorem for Additive Functionals of α-stable Processes

被引：1

作者：

Peszat, Szymon ^{[2
]}

Talarczyk, Anna ^{[1
]}

机构：

[1] Univ Warsaw, Inst Math, PL-02097 Warsaw, Poland

[2] Polish Acad Sci, Inst Math, PL-31027 Krakow, Poland

来源：

POTENTIAL ANALYSIS | 2010年 / 33卷 / 02期

关键词：

Functional limit theorem; Stable process; MARKOV-PROCESSES; TIMES;

D O I：

10.1007/s11118-009-9166-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let beta be a standard Brownian motion, let X be an alpha-stable process, and let f = (mu) over cap be the Fourier transform of a discrete measure. It is shown that weakly in C([0,+infinity)), eta(alpha/2) integral(t)(0) f (eta X(s))ds double right arrow root C(f,alpha)beta(t) as eta+infinity, or equivalently 1/root lambda integral(lambda t)(0) f(X(s))ds double right arrow root C(f,alpha)beta(t) as lambda+infinity.

引用

页码：199 / 209

页数：11

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