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

E. Bolthausen

Stochastic Processes and their Applications, 1984, vol. 16, issue 2, 199-204

Abstract: Let [xi]t, t [greater-or-equal, slanted] 0, be a d-dimensional Brownian motion. The asymptotic behaviour of the random field [latin small letter f with hook]|->[integral operator]t0[latin small letter f with hook]([xi]s) ds is investigated, where [latin small letter f with hook] 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.

Date: 1984
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