Timeline for What are the generalized Gaussian probability laws that are infinitely divisible?
Current License: CC BY-SA 3.0
5 events
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| May 16, 2014 at 0:23 | comment | added | Suvrit | Since the density function actually generates an infinitely divisible kernel---$\phi(x,y)^\alpha = \exp(-\alpha|x-y|^p)$ is ID---I believe we should be able to obtain a converse to conclude ID of the generalized Gaussian distribution; I hope you manage to work out the details (I gotta run). | |
| May 15, 2014 at 20:49 | comment | added | Goulifet | If I understand correctly the paper you suggest, the authors show that if a continuous and symmetric density is infinitely divisible, then the kernel you defined is positive-definite. In particular it shows that if $p>2$, the probability density that I defined is not infinitely-divisible. But, if I am not mistaken, I cannot say anything for $p<2$. Is there any kind of converse result to the one of the paper you gave? | |
| May 15, 2014 at 17:53 | comment | added | Suvrit | The following paper explorers this connection: arxiv.org/pdf/1403.7304 | |
| May 15, 2014 at 17:03 | comment | added | Noah Stein | Could you explain a bit about how positive definiteness of the kernel relates to infinite divisibility? | |
| May 15, 2014 at 16:48 | history | answered | Suvrit | CC BY-SA 3.0 |