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

21. 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 T = Min{t : X(t) = x}

= Min

t : B(t) = x − μt

σ

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