Hi,
I am considering brownian motion {B_t}in the interval (0,1) absorbed at 0 and 1. Now suppose that H is a continuous function on [0,1] and K is the smallest superharmonic (i.e.concave) function that dominates H on [0,1]. Can anyone give me ideas on how to prove that lim_t-->inf K(B_t) = lim_t-->inf H(B_t) a.s.?
Thanks
I am considering brownian motion {B_t}in the interval (0,1) absorbed at 0 and 1. Now suppose that H is a continuous function on [0,1] and K is the smallest superharmonic (i.e.concave) function that dominates H on [0,1]. Can anyone give me ideas on how to prove that lim_t-->inf K(B_t) = lim_t-->inf H(B_t) a.s.?
Thanks