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On the asymptotic behaviour of the empirical random field of the Brownian motion


Bolthausen, E (1984). On the asymptotic behaviour of the empirical random field of the Brownian motion. Stochastic Processes and their Applications, 16(2):199-204.

Abstract

Let ξt, t greater-or-equal, slanted 0, be a d-dimensional Brownian motion. The asymptotic behaviour of the random field ƒmaps to∫t0ƒ(ξs) ds is investigated, where ƒ belongs to a Sobolev space of periodic functions. Particularly a central limit theorem and a law of iterated logarithm are proved leading to a so-called universal law of iterated logarithm.

Abstract

Let ξt, t greater-or-equal, slanted 0, be a d-dimensional Brownian motion. The asymptotic behaviour of the random field ƒmaps to∫t0ƒ(ξs) ds is investigated, where ƒ belongs to a Sobolev space of periodic functions. Particularly a central limit theorem and a law of iterated logarithm are proved leading to a so-called universal law of iterated logarithm.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:central limit theorem; iterated logarithm law; uniform laws; additive functionals; Sobolev spaces
Language:English
Date:1984
Deposited On:19 Oct 2009 13:14
Last Modified:06 Dec 2017 21:17
Publisher:Elsevier
ISSN:0304-4149
Publisher DOI:https://doi.org/10.1016/0304-4149(84)90020-6
Related URLs:http://www.ams.org/mathscinet-getitem?mr=724115
http://www.zentralblatt-math.org/zmath/en/search/?q=an:0524.60024

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