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Results tagged with markov-chains
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user 81488
10
votes
"Surprising" examples of Markov chains
Let $S_n$ be the one-dimensional nearest neighbor random walk with $
1-q=p=P[S_{n+1}=x+1\mid S_n=x]=1-P[S_{n+1}=x-1\mid S_n=x]$,
where $p\neq q$. Then, there is a (rather surprising) fact that $Y_n=| …
- 1,897
1
vote
1
answer
108
views
Regularity of the entrance measure of SRW
Let $S(n)$ be the discrete sphere of radius $n$ (i.e., the internal boundary of the Euclidean discrete ball $B(n)$) centered in the origin, and consider a simple random walk starting at some $x\in\mat …
- 1,897
1
vote
Regularity of the entrance measure of SRW
We now have a proof of a weaker result (only Hölderness), see Proposition 1.3 of https://arxiv.org/abs/1606.05805 . The Lipschitzness is still beyond our reach...
- 1,897
5
votes
Random walk visiting a cylinder infinitely often
Well, for $d\geq 2$, the projection of $S_n$ onto a hyperplane orthogonal to $\vec{p}$ is a zero-mean $(d-1)$-dimensional random walk with bounded jumps. Therefore, the answer to your question is ''ye …
- 1,897
0
votes
The necessary sufficient condition for recurrence of a Markovian random walk
No, it's not sufficient, you need assumptions on the tails of $\sigma$'s. See Chapter 5 of http://www.ime.unicamp.br/~popov/book_lyapunov.pdf
- 1,897