OCCUPATION TIMES OF COMPACT-SETS BY PLANAR BROWNIAN-MOTION

Let K be a connected compact subset of R2. We consider the distribution of the occupation time (over the interval [0, tu]) of K by a Brownian motion started at an arbitrary point in R2. 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 Ito excursion law for the BES(2) process.