Open Access
June, 1973 Boundary Crossing Probabilities Associated with Motoo's Law of the Iterated Logarithm
Michael J. Wichura
Ann. Probab. 1(3): 437-456 (June, 1973). DOI: 10.1214/aop/1176996938


For certain recurrent diffusion processes, Motoo has given an integral test which allows one to determine whether an increasing function belongs to the upper or lower class relative to the process at hand. We show that a refinement of his methods yields asymptotic estimates for the tail probabilities of the time of last crossing of an upper class function $g$ in cases where the speed measure of the process has sufficiently thin tails and the curve $g$ increases sufficiently slowly. Similar results are derived for certain extremal processes and for non-decreasing stable processes.


Download Citation

Michael J. Wichura. "Boundary Crossing Probabilities Associated with Motoo's Law of the Iterated Logarithm." Ann. Probab. 1 (3) 437 - 456, June, 1973.


Published: June, 1973
First available in Project Euclid: 19 April 2007

zbMATH: 0281.60023
MathSciNet: MR373034
Digital Object Identifier: 10.1214/aop/1176996938

Primary: 60F15
Secondary: 60J25 , 60J60 , 60J65 , 60J75

Keywords: boundary crossing probabilities , Brownian motion , Diffusion processes , Law of the iterated logarithm , maxima and minima , Stable processes

Rights: Copyright © 1973 Institute of Mathematical Statistics

Vol.1 • No. 3 • June, 1973
Back to Top