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Results tagged with random-walks
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user 48831
3
votes
Probability of $\operatorname{Bin}(n,p)=\operatorname{Bin}(n,q)$ is decreasing when $n$ incr...
Here is a proof which also shows the exponential decay in $n$ for $p\neq q$
Let $0<p,q<1$ and $B_{n,p},B_{n,q}$ independent $\mathrm{Binomial}(n,p)$ resp. $\mathrm{Binomial}(n,q)$ distributed random v …
- 3,255
1
vote
Minimizer of two random walks
The topic belongs to the fluctuation theory
of random walks. See e.g. Feller II, 2nd ed. (1970), chapter XII.
Here is some useful (condensed) information:
(1) (for each $n$) the position of the (fi …
- 3,255
0
votes
The min of the mean of iid exponential variables
(Since you are looking for a reference, I turn my comment above into an answer:)
A proof using classical fluctuation theory is given my answer to
Expected supremum of average?
(I'm not aware that this …
- 3,255