Graduate School of Mathematical Sciences, The University of Tokyo
Journal of Mathematical Sciences, The University of Tokyo. Vol. 3 (1996), No. 1, Page 15-44
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.