Let W be a Brownian motion. Let Et(r) be the number of excursions of length larger than r that have been completed by time t. An excursion of length larger than r means that σf > r. Show that there...

Let W be a Brownian motion. Let Et(r) be the number of excursions of length larger than r that have been completed by time t. An excursion of length larger than r means that σf > r. Show that there exists a constant c such that

Determine c.

One interesting point here is that this shows that
  is determined entirely by the zero set

Chapter 28