An extension of a logarithmic form of Cramer's ruin theorem to some FARIMA and related processes

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:120

Article

Barbe, Ph.²  McCormick, W. P.¹ 

[1] Univ Georgia, Dept Stat, Athens, GA 30602 USA

[2] CNRS, UMR8088, F-75006 Paris, France

关键词: Maximum of random walk;    Cramer's theorem;    Fractional ARIMA process;    Ruin probability;    Large deviations;   

DOI  :  10.1016/j.spa.2010.02.001

来源: Elsevier

【 摘 要 】

Cramer's theorem provides an estimate for the tail probability of the maximum of a random walk with negative drift and increments having a moment generating function finite in a neighborhood of the origin. The class of (g, F)-processes generalizes in a natural way random walks and fractional ARIMA models used in time series analysis. For those (g, F)-processes with negative drift, we obtain a logarithmic estimate of the tail probability of their maximum, under conditions comparable to Cramer's. Furthermore, we exhibit the most likely paths as well as the most likely behavior of the innovations leading to a large maximum. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free