HURST INDEX OF FUNCTIONS OF LONG-RANGE-DEPENDENT MARKOV CHAINS

被引：0

作者：

Oguz, Barlas ^{[1
]}

Anantharam, Venkat ^{[1
]}

机构：

[1] Univ Calif Berkeley, Dept Elect Engn & Comp Sci, Berkeley, CA 94720 USA

来源：

JOURNAL OF APPLIED PROBABILITY | 2012年 / 49卷 / 02期

基金：

美国国家科学基金会;

关键词：

Markov chain; long-range dependence; Hurst index;

D O I：

暂无

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：

A positive recurrent, aperiodic Markov chain is said to be long-range dependent (LRD) when the indicator function of a particular state is LRD. This happens if and only if the return time distribution for that state has infinite variance. We investigate the question of whether other instantaneous functions of the Markov chain also inherit this property. We provide conditions under which the function has the same degree of long-range dependence as the chain itself. We illustrate our results through three examples in diverse fields: queueing networks, source compression, and finance.

引用

页码：451 / 471

页数：21

共 14 条

[1]

Barron A.R., 1985, THESIS STANFORD U

[2] LONG-RANGE DEPENDENCE IN VARIABLE-BIT-RATE VIDEO TRAFFIC [J].

BERAN, J ;

SHERMAN, R ;

TAQQU, MS ;

WILLINGER, W .

IEEE TRANSACTIONS ON COMMUNICATIONS, 1995, 43 (2-4) :1566-1579

[3]

Bingham NH., 1989, REGULAR VARIATION

[4] Long-range dependence of Markov chains in discrete time on countable state space [J].

Carpio, K. J. E. ;

Daley, D. J. .

JOURNAL OF APPLIED PROBABILITY, 2007, 44 (04) :1047-1055

[5]

Chung K.L., 1967, Markov Chains with Stationary Transition Probabilities, Vsecond

[6] Empirical properties of asset returns: stylized facts and statistical issues [J].

Cont, Rama .

QUANTITATIVE FINANCE, 2001, 1 (02) :223-236

[7] MPEG-4 and H.263 video traces for network performance evaluation [J].

Fitzek, FHP ;

Reisslein, M .

IEEE NETWORK, 2001, 15 (06) :40-54

[8]

Garett M.W., 1994, P ACM SIGCOMM, P269

[9]

Giraitis L, 2000, ANN APPL PROBAB, V10, P1002

[10] Second-order noiseless source coding theorems [J].

Kontoyiannis, I .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1997, 43 (04) :1339-1341

← 1 2 →