The point process approach for fractionally differentiated random walks under heavy traffic

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:122

Article

Barbe, Ph.²  McCormick, W. P.¹ 

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

[2] CNRS, UMR 8088, F-75006 Paris, France

关键词: Heavy traffic;    Point process;    Supremum functional;    Fractional random walk;    FARIMA process;    Poisson process;   

DOI  :  10.1016/j.spa.2012.08.008

来源: Elsevier

【 摘 要 】

We prove some heavy-traffic limit theorems for some nonstationary linear processes which encompass the fractionally differentiated random walk as well as some FARIMA processes, when the innovations are in the domain of attraction of a non-Gaussian stable distribution. The results are based on an extension of the point process methodology to linear processes with nonsummable coefficients and make use of a new maximal type inequality. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free