The small-time Chung-Wichura law for Levy processes with non-vanishing Brownian component

被引：4

作者：

Buchmann, Boris ^{[1
]}

Maller, Ross ^{[2
]}

机构：

[1] Monash Univ, Sch Math Sci, Clayton, Vic 3800, Australia

[2] Australian Natl Univ, Ctr Math & Applicat, Sch Finance & Appl Stat, Canberra, ACT, Australia

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2011年 / 149卷 / 1-2期

基金：

澳大利亚研究理事会;

关键词：

Levy process; Local behaviour; Almost sure convergence; Iterated logarithm laws; Other law of the iterated logarithm; Cluster sets; Functional limit theorem; SMALL BALL PROBABILITIES; FUNCTIONAL LIL; STRASSEN;

D O I：

10.1007/s00440-009-0255-1

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We give a "small time" functional version of Chung's "other" law of the iterated logarithm for L,vy processes with non-vanishing Brownian component. This is an analogue of the "other" law of the iterated logarithm at "large times" for L,vy processes and random walks with finite variance, as extended to a functional version by Wichura. As one of many possible applications, we mention a functional law for a two-sided passage time process.

引用

页码：303 / 330

页数：28

共 36 条

[1]

Anderson T. W., 1955, Proc. Amer. Math. Soc., V6, P170

[2]

[Anonymous], J MATH SCI

[3] SMALL DEVIATIONS OF GENERAL LEVY PROCESSES [J].

Aurzada, Frank ;

Dereich, Steffen .

ANNALS OF PROBABILITY, 2009, 37 (05) :2066-2092

[4] Passage of levy processes across power law boundaries at small times [J].

Bertoin, J. ;

Doney, R. A. ;

Maller, R. A. .

ANNALS OF PROBABILITY, 2008, 36 (01) :160-197

[5]

Bertoin J., 1996, Cambridge Tracts in Mathematics, V121

[6]

BINGHAM NH, 1986, B LOND MATH SOC, V18, P432

[7] An almost sure functional limit theorem at zero for a class of Levy processes normed by the square root function, and applications [J].

Buchmann, Boris ;

Maller, Ross ;

Szimayer, Alex .

PROBABILITY THEORY AND RELATED FIELDS, 2008, 142 (1-2) :219-247

[8]

Chen X, 2000, ANN PROBAB, V28, P258

[9]

CHUNG KL, 1948, T AM MATH SOC, V64, P205

[10] A RELATION BETWEEN CHUNGS AND STRASSENS LAWS OF THE ITERATED LOGARITHM [J].

CSAKI, E .

ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1980, 54 (03) :287-301

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