Timeline for Which random walk can generate gamma distribution in the limit?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Sep 22, 2019 at 14:32 | comment | added | david | Thank you again. | |
| Sep 22, 2019 at 4:02 | comment | added | Iosif Pinelis | @david : The only difference is in form (and in using $s$ in the latter expression rather than $r$) but not in the actual value. You can easily transform one form to the other. The two different forms of the same expression serve the two different purposes: (i) to find the limit and (ii) to expand into powers of $e^{it}$. | |
| Sep 20, 2019 at 23:44 | comment | added | david | @losif: why $f_{p,s}(t)=(1/q-e^{it}p/q)^{-s}$ is different from $f_{p,r}$ as in (1) in your original answers ? | |
| Sep 20, 2019 at 22:04 | comment | added | david | Thank you again. | |
| Sep 20, 2019 at 21:45 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Sep 20, 2019 at 21:32 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Sep 20, 2019 at 21:28 | comment | added | Iosif Pinelis | @david : Yes, this can be done and is now done in the answer. | |
| Sep 20, 2019 at 21:27 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Sep 20, 2019 at 20:57 | comment | added | david | Can $qX_{p,r}$ be written as the sum of iid random variables ? such as: $qX_{p,r} = x_1 + x_2 + ... + x_n$ where each $x_k$ is a random variable ? | |
| Sep 20, 2019 at 19:30 | comment | added | Iosif Pinelis | @david : Multiplying $X_{p,r}$ by $q$ means time re-scaling, namely, replacing the unit time step in the original Bernoulli series by time step $q$. Letting then $q$ be small means that we make the time step small and, simultaneously and accordingly, make the failure probability small at each of the small time steps. | |
| Sep 20, 2019 at 19:12 | comment | added | david | Thank you. Condition "Letting now $p\uparrow1$, so that $q\downarrow0$ " is interesting. | |
| Sep 20, 2019 at 18:58 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |