The tail probability of the first hitting time is discussed for linear diffusions. We obtain the decay rates in terms of the spectral functions and the scale functions. The result is a generalization of recent results of Hamana-Matsumoto for Bessel processes.
"Tails of the first hitting times of linear diffusions." Tsukuba J. Math. 40 (1) 55 - 79, July 2016. https://doi.org/10.21099/tkbjm/1474747487