21. Let {X(t), t 0} be Brownian motion with drift coefficient and variance parameter 2. That...
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21. Let {X(t), t 0} be Brownian motion with drift coefficient μ and variance parameter
σ2. That is,
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:
X(t) =B(t) + ut Let 0, and for a positive constant x let > T Min{t: X(t) = x) Min{t: = Mint: B(t) = x-ut
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