  A regime-switching geometric Brownian motion is used to model a geometric
Brownian motion with its coefficients changing randomly according to a Markov
chain. In this work, we give a complete characterization of the recurrent
property of this process. The long time behavior of this process such as its
$p$-th moment is also studied. Moreover, the quantitative properties of the
regime-switching geometric Brownian motion with two-state switching are
investigated to show the difference between geometric Brownian motion with
switching and without switching. At last, some estimates of its first passage
probability are established.
