Timeline for What is the asymptotic behavior of the Levy distribution $P (x)$ when the independent variable $x$ approaches $0$
Current License: CC BY-SA 4.0
8 events
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| Sep 14, 2023 at 10:37 | comment | added | Carlo Beenakker | Taylor expansion works because the integral is dominated by the small-$q$ region; as a check, I added the cases $\alpha=1$ and $\alpha=2$, which can be evaluated in closed form. | |
| Sep 14, 2023 at 10:37 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Sep 14, 2023 at 10:32 | comment | added | Carlo Beenakker | for $\alpha\leq 0$ the integral is divergent | |
| Sep 14, 2023 at 9:01 | comment | added | 吴月红 | Thank you, because q is taking from 0 to infinite ,does not Taylor expansion work? what is more ,if \alpha is less than 0 , the result of integral? | |
| Sep 14, 2023 at 8:54 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Sep 14, 2023 at 8:51 | comment | added | Carlo Beenakker | yes, assuming $\gamma>0$ and $\alpha>0$ so that the integral converges | |
| Sep 14, 2023 at 8:50 | comment | added | 吴月红 | Thank you! Did you calculate this integral with Taylor expansion? | |
| Sep 14, 2023 at 8:43 | history | answered | Carlo Beenakker | CC BY-SA 4.0 |