Krishna Athreya
Iowa State University

What is Brownian motion?

A simple answer is it is a Gaussian process on [0, infinity] with  mean function zero  and covariance  function min s and t N. Wiener gave an alternate construction via iid N(0,1) rv and a complete ortho normal  set in L2{0,1] that had the right distribution and the trajectories that are continuous but not differentiable. We describe this and give a few properties. We also give an ergodic thm due to G. Kallianpur and H. Robbins. We conclude with an application to European option pricing formula or stocks.

Refreshments at 3:45pm in Snedecor 2101.