Timeline for Determine the affine envelope of a random process's MGF
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 23, 2021 at 22:25 | vote | accept | leeyee | ||
| Dec 23, 2021 at 2:42 | answer | added | Iosif Pinelis | timeline score: 1 | |
| Dec 22, 2021 at 19:09 | history | edited | LSpice | CC BY-SA 4.0 |
Typo (envelop -> envelope), and other minor TeXing
|
| Dec 22, 2021 at 16:29 | history | edited | Iosif Pinelis |
edited tags
|
|
| Dec 21, 2021 at 3:10 | answer | added | Iosif Pinelis | timeline score: 1 | |
| Dec 17, 2021 at 20:51 | comment | added | Iosif Pinelis | I will try to find time to write down an answer. | |
| Dec 17, 2021 at 15:00 | comment | added | leeyee | @IosifPinelis Yes, $D_i$'s are iid. | |
| Dec 17, 2021 at 12:20 | comment | added | Iosif Pinelis | Are the $D_i$'s iid? | |
| Dec 17, 2021 at 4:39 | comment | added | leeyee | @IosifPinelis Yes, $D_i$'s are independent of $B_i$'s. We may think of $B_i$'s as the busy period of a queueing system. It occurs when a customer arrives at the empty system. In the current setting, I'm trying to not assume a specific arrival pattern. | |
| Dec 17, 2021 at 3:38 | history | edited | leeyee | CC BY-SA 4.0 |
Added an attempted solution
|
| Dec 17, 2021 at 1:39 | comment | added | Iosif Pinelis | The setting is still not quite clear to me. Can you define it formally? Say, can we assume that the beginning of the $i$th stalling period is $D_1+B_1+D_2+\cdots+B_{i-1}+D_i$, where the $D_i$'s are iid independent of $B_i$'s? If so, what else do we know about the durations $D_i$? | |
| Dec 17, 2021 at 1:16 | history | edited | leeyee | CC BY-SA 4.0 |
clarified conditions
|
| Dec 17, 2021 at 1:11 | comment | added | leeyee | @Iosif Pinelis Thanks for reminding this important point. The appearance of $B_i$'s is a renewal process. In a fraction of $\rho$ time the system may see a $B_i$. Let $N(t)$ denote the number of $B_i$'s in a duration of time $t$. Using renewal theory, the appearance frequency of $B_i$'s is approximately $\lim_{t\rightarrow \infty}\frac{N(t)}{t}=\lim_{t\rightarrow\infty}\frac{\rho t/\mathrm{E}[B]}{t}=\frac{\rho}{\mathrm{E}[B]}$. I have updated the question. | |
| Dec 16, 2021 at 15:00 | comment | added | Iosif Pinelis | What do you mean by "occasionally"? How often do these occasions come? In what way -- by themselves and in relation with the $B_i$'s? | |
| Dec 16, 2021 at 13:17 | history | edited | leeyee | CC BY-SA 4.0 |
fixed grammar and refined tags
|
| Dec 16, 2021 at 9:46 | history | asked | leeyee | CC BY-SA 4.0 |