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