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Zbl 0796.60083
Chan, Terence
Occupation times of compact sets by planar Brownian motion. (English)
[J] Ann. Inst. Henri Poincaré, Probab. Stat. 30, No.2, 317-329 (1994). ISSN 0246-0203

Summary: Let $K$ be a connected compact subset of ${\bbfR}\sp 2$. We consider the distribution of the occupation time (over the interval $[0,t]$) of $K$ by a Brownian motion started at an arbitrary point in ${\bbfR}\sp 2$. We obtain an explicit formula for the distribution of the occupation time of a closed disc by a Brownian motion. Using this result, we then obtain some Tauberian asymptotic results for the general case. The main technique involves calculating the Itô excursion law for the BES(2) process.

MSC 2000:: *60J65 Brownian motion
60F99 Limit theorems (probability)

Keywords: arc-sine law; Brownian motion; occupation time; Tauberian asymptotic results; Itô excursion law

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