  We recover in part a recent result of Hamana-Matsumoto (2014) on the
asymptotic behaviors for tail probabilities of first hitting times of Bessel
process. Our proof is based on a weak convergence argument. The same reasoning
enables us to derive the asymptotic behaviors for the tail probability of the
time at which the global infimum of Bessel process is attained, and for
expected values relative to local infima. In addition, we give another proof of
the result of Hamana-Matsumoto with improvement of error estimates, which
complements in the case of noninteger dimensions the asymptotic formulae by van
den Berg (2007) for first hitting times of multidimensional Brownian motion.
