On the asymptotic behaviour of the empirical random field of the brownian motion |
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Authors: | E. Bolthausen |
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Affiliation: | Technische Universität Berlin, 1000 Berlin 12, W. Germany |
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Abstract: | Let ξt, t ? 0, be a d-dimensional Brownian motion. The asymptotic behaviour of the random field ??∫t0?(ξs) ds is investigated, where ? 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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Keywords: | 60J65 60F05 60F15 60J55 |
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