Suppose is a two-dimensional Brownian motion, and r > 0. Imitate the argument of Proposition 21.1 but with to show that Then use the strong Markov property to show that there are times That is,...

Suppose

is a two-dimensional Brownian motion, and r > 0. Imitate the argument of Proposition 21.1 but with

to show that

Then use the strong Markov property to show that there are times

That is, two-dimensional Brownian motion is neighborhood recurrent.