Timeline for Approximate CDF of integral using the Berry-Esseen theorem
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 12 at 12:55 | comment | added | Paul R | @IosifPinelis , thank you very much! | |
| Jan 11 at 22:33 | comment | added | Iosif Pinelis | This joint distribution is the bivariate normal distribution with the marginals as in your previous comment and with correlation $1/\sqrt2$, as I mentioned previously. | |
| Jan 11 at 9:43 | comment | added | Paul R | @IosifPinelis , what is the joint distribution in this case? | |
| Jan 10 at 22:49 | comment | added | Iosif Pinelis | The correlation, say between $X$ and $Y$, is about the joint distribution of $X$ and $Y$. The individual distributions of $X$ and of $Y$ can tell you nothing about their correlation. | |
| Jan 10 at 21:40 | comment | added | Paul R | Can you explain why? I thought that $W_{\frac{T}{N}}\sim N\left(0,\frac{T}{N}\right)$ and $W_{\frac{2T}{N}}\sim N\left(0,\frac{2T}{N}\right)$. I don't see correlation between them. | |
| Jan 10 at 21:38 | comment | added | Iosif Pinelis | Your summands are not increments of the Wiener process. In particular, the random variables $W_{T/N}$ and $W_{2T/N}$ are correlated (with correlation coefficient $1/\sqrt2$) and hence (positively) dependent. | |
| Jan 10 at 21:30 | comment | added | Paul R | @IosifPinelis , why are they independent? Wiener process has independent increments: en.wikipedia.org/wiki/… | |
| Jan 10 at 21:29 | comment | added | Iosif Pinelis | This application of the Berry--Esseen inequality is incorrect -- because that inequality is for sums of indepedendent random summands, whereas your summands are not independent. | |
| Jan 10 at 21:16 | history | asked | Paul R | CC BY-SA 4.0 |