The Vervaat process in Lp spaces

JOURNAL OF MULTIVARIATE ANALYSIS

卷:78

Article

Csörgö, M ; Zitikis, R

关键词: Vervaat process;    empirical process;    quantile process;    Bahadur-Kiefer process;    Kiefer process;    Brownian bridge;    Wiener process;    L-p-space;    the law of the iterated logarithm;    convergence in distribution;   

DOI  :  10.1006/jmva.2000.1941

来源: Elsevier

【 摘 要 】

It is well known that, asymptotically, the appropriately normalized Vervaat process behaves like one half times the squared empirical process, Considering these two processes as elements of the L-p-space, 1 less than or equal top < we give a complete description of the strong and weak asymptotic behaviour of the L-p-distance between them, and thus of the L-p-norm of the Vervaat process as well. The herein obtained results also raise a number of further mathematical and probabilistic problems which we formulate as suggestions for future consideration. (C) 2001 Academic Press.

【 授权许可】

Free