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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.
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.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > Statistics and Probability
Physical Sciences > Modeling and Simulation Physical Sciences > Applied 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: | 03 Jan 2025 02:39 |
| Publisher: | Elsevier |
| ISSN: | 0304-4149 |
| OA Status: | Closed |
| 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 |
Bolthausen, E