Use the reflection principle to prove that if W is a Brownian motion and (0,∞)}, then In other words, Brownian motion enters the interval (0,∞) immediately. By symmetry it enters the interval (−∞,...

Use the reflection principle to prove that if W is a Brownian motion and

(0,∞)}, then

In other words, Brownian motion enters the interval (0,∞) immediately. By symmetry it enters the interval (−∞, 0) immediately. Conclude that Brownian motion hits 0 infinitely often in every time interval [0,t].