How does one get to this result in the Course notes: For a Wiener process Wt: lim t-> inf [Wt/t] = lim t-> inf [W_{1/t}]
We can verify that W*(t) = t W(1/t) is a standard Brownian motion by showing it has: - 0 mean - normally distributed increments - cov(W*(t),W*(s)) = min(t,s) and therefore W(1/t) is the same as W*(t)/t These 3 bullet points are an alternative definition of standard Brownian motion and you should have a go at showing the last one - it's 3 lines of algebra and quite good fun! Good luck! John
