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Strong markov property on max of brownian motion
For $B_t$ Brownian Motion with drift $\mu<0$, I have the max value, $X = \max_{0<t<\infty}B_t$ .
I need to prove with the Strong Markov Property that, $P(X>c+d)=P(X>c)P(X>d)$
a. It ...
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Max of Brownian motion with drift is finite almost surely
For $B_t$ Brownian Motion with drift $\mu<0$, I need to prove that the max value, $X = \max_{0<t<\infty}B_t$ is finite almost surely, ie $P(X<\infty)=1$.
Now, I know that because the mean ...
