# Expectation of number of hits by a brownian motion

If we denote $$\tau_i$$ the sequence of stopping times defined by: $$\tau_i = \inf(t>\tau_{i-1} : |B(t)-B(\tau_{i-1})| > a)$$, $$\tau_0=0$$.

If we denote N the number of stopping times below T.

What is the expectation of N (i.e. the average number of stopping times below T)?