Random Walk's Stochastic Wave

Click here to see the Stochastic Waves paper I wrote with Dynkin in 1982.

The ordinary random walk is shown in blue. The gold curve shows first visits to x = 0, 1, 2, 3, ... and the orange curve shows first visits to x = 0, -1, -2, -3, ... . These are two stochastic waves from the same random walk.

Click here for a Brownian motion version.