  This work focuses on stability of regime-switching diffusions consisting of
continuous and discrete components, in which the discrete component switches in
a countably infinite set and its switching rates at current time depend on the
continuous component. In contrast to the existing approach, this work provides
more practically viable approach with more feasible conditions for stability. A
classical approach for asymptotic stabilityusing Lyapunov function techniques
shows the Lyapunov function evaluated at the solution process goes to 0 as time
$t\to \infty$. A distinctive feature of this paper is to obtain estimates of
path-wise rates of convergence, which pinpoints how fast the aforementioned
convergence to 0 taking place. Finally, some examples are given to illustrate
our findings.
