Publication: On the asymptotic behaviour of the empirical random field of the Brownian motion
On the asymptotic behaviour of the empirical random field of the Brownian motion
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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, 199–204. https://doi.org/10.1016/0304-4149(84)90020-6
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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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- Bolthausen, E
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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, 199–204. https://doi.org/10.1016/0304-4149(84)90020-6