Let {X(t), t 0} be Brownian motion with drift coefficient and variance parameter 2. That

Let {X(t), t ≥ 0} be Brownian motion with drift coefficient μ and variance parameter σ2. That is, X(t) = σB(t)+ μt Let μ>0, and for a positive constant x let

That is, T is the first time the process {X(t), t ≥ 0} hits x. Use the Martingale stopping theorem to show that E[T] = x/μ

Transcribed Image Text:

T=Min{t: X(t)=x} in{r: Mint: B(t): x-t =