Timeline for Recurrence of Poisson binomial distributed random walk
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 19, 2015 at 9:20 | vote | accept | user45947 | ||
| Oct 20, 2015 at 8:21 | |||||
| Oct 19, 2015 at 9:20 | comment | added | user45947 | A valuable answer anyway. Thanks for chipping in. | |
| Oct 19, 2015 at 9:17 | comment | added | Dan Romik | No, sorry... :-( | |
| Oct 19, 2015 at 9:06 | comment | added | user45947 | I'm obviously interested in what this subtle condition would be. You say it's not an obvious question, but do you anyhow happen to know some references that at least partly addresses it? | |
| Oct 19, 2015 at 8:46 | comment | added | Dan Romik | You will need a more subtle condition, since if the $p_n$'s are very close to 1 rather than 0 then you won't get recurrence for similar reasons, and if many of them are close to 0 and many are close to 1, you can arrange to have or not have recurrence by choosing how you alternate the near-zeros with the near-ones. Also for a full analysis you may need to separate the case when $S_n$ takes values on a lattice (e.g. when $p_n=c$ for some rational constant $c$) from the non-lattice case, since those two cases involve different definitions of recurrence. So it's not an obvious question. | |
| Oct 19, 2015 at 8:21 | comment | added | user45947 | Thanks. I didn't think of extreme cases like that. Is it the case that any sequence of probabilities $p_n$ that satisfies $\lim_{n \to \infty} \sum_n p_n = \infty$ would yield $S_n$ recurrent? It certainly is true for $p_n = 1/2$, but would it be true for example for $p_n = 1/n$? | |
| Oct 19, 2015 at 7:53 | history | answered | Dan Romik | CC BY-SA 3.0 |