Martingales and first passage times of AR(1) sequences

被引：18

作者：

Novikov, Alexander ^{[1
]}

Kordzakhia, Nino ^{[2
]}

机构：

[1] Univ Technol Sydney, Dept Math Sci, Sydney, NSW 2007, Australia

[2] Macquarie Univ, Dept Stat, Sydney, NSW 2109, Australia

来源：

STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES | 2008年 / 80卷 / 2-3期

关键词：

first passage times; autoregressive processes; martingales; exponential boundedness;

D O I：

10.1080/17442500701840885

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Using the martingale approach we find sufficient conditions for exponential boundedness of first passage times over a level for ergodic first order autoregressive sequences. Further, we prove a martingale identity to be used in obtaining explicit bounds for the expectation of first passage times.

引用

页码：197 / 210

页数：14

共 18 条

[11] KYPRIANOU AE, 2006, INTR LECT FLUCT LEV
[12] First passage time of filtered Poisson process with exponential shape function
Novikov, A
Melchers, RE
Shinjikashvili, E
Kordzakhia, N
[J]. PROBABILISTIC ENGINEERING MECHANICS, 2005, 20 (01) : 57 - 65
[13] ON THE 1ST PASSAGE TIME OF AN AUTOREGRESSIVE PROCESS OVER A LEVEL AND AN APPLICATION TO A DISORDER PROBLEM
NOVIKOV, AA
[J]. THEORY OF PROBABILITY AND ITS APPLICATIONS, 1990, 35 (02) : 269 - 279
[14] NOVIKOV AA, 1993, P STEKLOV I MATH, V202, P169
[15] NOVIKOV AA, 2006, LECT NOT C STOCH CAL
[16] A Markov chain model for the multivariate exponentially weighted moving averages control chart
Runger, GC
Prabhu, SS
[J]. JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 1996, 91 (436) : 1701 - 1706
[17] Sukparungsee S., 2006, KMITL Sci. J.: Int. J. Sci. Appl. Sci, V6, P373
[18] STOCHASTIC DIFFERENCE EQUATION AND A REPRESENTATION OF NONNEGATIVE INFINITELY DIVISIBLE RANDOM-VARIABLES
VERVAAT, W
[J]. ADVANCES IN APPLIED PROBABILITY, 1979, 11 (04) : 750 - 783

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