Let $B_t$ be a standard Brownian motion process starting at $B_0=0$.

For $c,\delta>0$ and some function $F(t)$, I am considering the following

$\lim_{t\rightarrow \infty} \frac{e^{ct}P(|B_t|>\delta t)}{F(t)}=1$.

I need to prove the above.


closed as unclear what you're asking by zhoraster, Yanior Weg, Lee David Chung Lin, Ak19, Cesareo Jun 15 at 9:43

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    $\begingroup$ "I found it to be finite" -- certainly depends on $F$. But everything is pretty computable, please write where exactly do you have a problem. $\endgroup$ – zhoraster Jun 12 at 12:44
  • $\begingroup$ Could you please state clarly what exactly you want to prove? If you just pick some function $F$, then the assertion is certainly wrong $\endgroup$ – saz Jun 12 at 18:01