Some asymptotic formulae for Bessel process

#### Y. Hariya

2015, v.21, Issue 2, 293-316

ABSTRACT

We recover in part a recent result of Hamana and Matsumoto \cite{hm} 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
\cite{hm} with improvement of error estimates, which complements
in the case of noninteger dimensions the asymptotic formulae by van den Berg
\cite{vdb} for first hitting times of multidimensional Brownian motion.

Keywords: Bessel process; tail probability; weak convergence