Timeline for Running minimum of exponential random walks
Current License: CC BY-SA 4.0
3 events
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| Apr 18 at 10:52 | comment | added | van der Wolf | By the general invariance principle, for $t\in[0,1]$ and $n\to\infty$ $$ \frac{S_{\lfloor nt\rfloor}-\lfloor nt\rfloor}{\sqrt{n}}\to B_t $$ where $B_t$ is a Brownian motion. Therefore, $\frac{S_{k}-k}{\sqrt k}\asymp\frac{B_t}{\sqrt{t}}$ for $k\le n$ and $t=k/n$. So we are interested in $$ \sup_{t\in(0,1]} \frac{B_t}{\sqrt t} $$ So this is relevant to math.stackexchange.com/questions/1856443/… but alas the discrete time answer must be different... | |
| Apr 10 at 6:19 | history | edited | Xiao | CC BY-SA 4.0 |
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| Apr 9 at 22:45 | history | asked | Xiao | CC BY-SA 4.0 |