Timeline for Growth rate of exponential sum of $S_j$
Current License: CC BY-SA 4.0
5 events
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| Oct 27, 2020 at 9:39 | comment | added | Mini | The case of $\alpha=0$ is the common random walk and for this case it trivially holds. When $C_i=1$ also the simulations suggest that it holds also. Actually in this case, $\frac{1}{n}g(n)$ would have some drift around the curve $\frac{1}{\sqrt{n}}$. | |
| Oct 27, 2020 at 0:24 | comment | added | Anthony Quas | If you write down $g(n)\overline{g(n)}$ and expand, you obtain $g(n)\overline g(n)=n+2\sum_{j<k}\text{Re}\big(c_k\bar c_j\exp(\frac 1{n^\alpha}S_j^k)\big)$, where $S_j^k$ is $S_k-S_j$. If $X_i$ is mean 0, I don't think the variance of $g(n)$ is finite. For the case where the mean is positive, you're probably OK. | |
| Oct 26, 2020 at 21:06 | history | edited | Mini | CC BY-SA 4.0 |
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| Oct 26, 2020 at 19:37 | history | edited | YCor |
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| Oct 26, 2020 at 19:35 | history | asked | Mini | CC BY-SA 4.0 |