
Markov Property
one more question,
I am rereading a lecture and i come across the following:
define escape time as $\displaystyle \xi_r=inf[t>0  (X_tX_0>r)]$
now my notes say that is easy to show by using markov property that $\displaystyle P[\xi_r \geq nt]\leq p^n$ for n=0,1,..
By the time i must have thought it was easy, now i cant remember how to do it anymore :(

i found it again:
$\displaystyle P[\xi_r \geq nt]\leq P_x \cap_{k\leq n}[X_{kt} \in B_x(r)]=(P_t^d[x \in B_x(r)])^n \leq p^n$ where B_x(r) is closed ball of radius r around x