First exit time: continuation). Prove the claim of Example 2.9: show that τ[a,b] is a Markov time for the Brownian motion.
There are two slightly different concepts of a signed measure, depending on whether one allows it to take infinite values (see, e.g., Wikipedia).
(First exit time). The first exit time from an interval is a Markov time for the Brownian motion. It is defined for a < 0="">< b="">