0
$\begingroup$

Many properties of Brownian motion have been extended to SSP's for $0\leq \alpha\leq 2$ and so it is quite easy to find literature on them. However, I am currently studying the SSP for $\alpha>2$ in the context of isoperimetric inequalities, and I came here because I found it hard getting any references,surveys and textbooks.

Here is the wikipedia article: http://en.wikipedia.org/wiki/Stable_distribution.

The motivation is in http://www.ams.org/journals/tran/2004-356-02/S0002-9947-03-03298-7/S0002-9947-03-03298-7.pdf

On page 736 "Theorem 1: Among all compact sets K in Rn with given volume, the balls have the least α-capacity (0 <α< 2)."

Then underneath theorem 1, the author mentions that the problem is open for $\alpha\in (2,n)$ where $n\geq 3$.

Thank you

So far:

1.(short note on Levy processes) http://galton.uchicago.edu/~lalley/Courses/385/LevyProcesses.pdf

$\endgroup$
2
  • $\begingroup$ Isn't it a standard theorem that there only exist $\alpha$-stable distributions for $0 < \alpha \le 2$? So wouldn't that mean there is no such thing as a symmetric $\alpha$-stable process with $\alpha > 2$? $\endgroup$ Feb 18, 2015 at 3:30
  • $\begingroup$ @Nate interesting; do they have name? I wish in the linked paper, the author made that clear. $\endgroup$
    – TKM
    Feb 18, 2015 at 20:05

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.