Long run behavior of a dynamical system

Long run behavior of a dynamical system

pI have to deal with a dynamical system that looks as follows, with $H$
being the initial state (parameters next to arrows denote transition
probabilities between the states $H$, $L_1$ and $L_2$):/p pimg
src=http://i.stack.imgur.com/EqrTE.png alt=enter image description here/p
pI must admit that I have not much clue how to analyze such a system. I
would be interested in two basic questions:/p p(1) If we let the dynamical
system run for a long while (as the number of periods $T=1,2,3,...$ goes
to infinity), which fraction of the time will be spent in each of the 3
states?/p p(2) Conditional on having a switch from either $L_1$ or $L_2$
to $H$, which fraction of the time do we experience a switch from $L_2$ to
$H$?/p pAny answers how to deal with that problem would be most welcome.
Thanks in advance!/p