# Convergence of reflected Brownian motion [closed]

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, CesareoJun 15 at 9:43

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