Timeline for Minimizer of two random walks
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 29, 2017 at 17:10 | comment | added | Oliver | Right, I think I get it now :-) Thanks! | |
| May 26, 2017 at 18:11 | comment | added | esg | (1) Yes, they do match. The book treats ascending ladder epochs/no. of positive terms, the formula above rewrites that for descending ladder epochs/no. of negative terms. (2) Yes, that's what I meant. | |
| May 25, 2017 at 19:23 | comment | added | Oliver | (1)It's a little weird since on the book, XII.7 Theorem 1 states that $\log \frac {1}{1-\tau(s)} = \sum_{i=1}^\infty \frac {s^n}{n}\mathbb{P}\{S_n>0\}$. And those two doesn't seem to match. Anyway, I'll check that paper also. (2) So I guess what you meant was $\delta/\sigma$ is the only parameter? Not the 'scale parameter' in the statistical 'scale family' sense? | |
| May 23, 2017 at 16:11 | comment | added | esg | (i) the formula in (2) is another consequence of the Sparre Andersen transformation, see e.g. Theorem 4.4 here (ii) "kind of rescale" leaves room for interpretation. I just meant the fact that exchanging the "scale parameter" $\frac{\delta^2}{\sigma^2}$ transforms one distribution into the other. | |
| May 22, 2017 at 21:47 | comment | added | Oliver | Thanks a lot for the information! I checked the related chapters in the book, however I do have some questioned about the answer you wrote above. In $(2)$, how did you get the generating function $g(z)$? It seems that this was a little different than what the book had. Also, in $(3)$, we know that $g(z)$ is a function only of $\frac{\delta}{\sigma}$, but from that how can we tell that the two distributions are scaled versions of each other? | |
| May 19, 2017 at 18:01 | history | answered | esg | CC BY-SA 3.0 |