## Notes on the integrability of exit times from unbounded domains of Brownian motion

J. Math. Sci. Univ. Tokyo
Vol. 3 (1996), No. 1, Page 15--44.

Atsuji, Atsushi
Notes on the integrability of exit times from unbounded domains of Brownian motion
The integrability and the tail distribution of the first exit time from unbounded domain of Brownian motions will be considered. They are characterized by the growth order of the first eigen values of the intersection of domains and sphere with radius $r$ and quasi-hyperbolic distance.