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The Vervaat Process in Lp Spaces

✍ Scribed by Miklós Csörgő; Ričardas Zitikis

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
251 KB
Volume
78
Category
Article
ISSN
0047-259X

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✦ Synopsis

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 p< , 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.

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