Timeline for Asymptotic properties of weighted random walks / infinite convolutions of random variables
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
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| Jan 19, 2023 at 10:55 | comment | added | mike | just throw in some mass at -1. The negative part will actually have a finite sum & so cannot affect the convergence or divergence of the whole sum | |
| Jan 19, 2023 at 10:13 | comment | added | SetofMeasureZero | Thanks, I see that $P(X>c^{-k})>\frac{1}{k}$ would yield $\lim\limits_{n\to\infty}\sum_{k=1}^nc^kX_k=\infty$ a.s., if $X\geq 0$ a.s. So your example definitely works perfectly fine. Do you know by any chance a method to construct such examples, if we drop the assumption, that $X\geq 0$ a.s.? | |
| Jan 19, 2023 at 6:09 | history | answered | mike | CC BY-SA 4.0 |