Some remarks on stable stochastic processes and $\alpha$-superharmonic functions

An integral representation is established for a stable multidimensional probability density. It is used for a new and direct proof of the fact that anagr-superharmonic function considered on the trajectories of a stable symmetric stochastic process with parameter a is a super-martingale. It is moreover established that the stable density belongs to the convex cone generated by the functions $\varepsilon_\alpha^{(r)}(x)$ of M. Riesz.