Geodesic
Some remarks on stable stochastic processes and $\alpha$-superharmonic functions
Matematičeskie zametki, Tome 14 (1973) no. 6, pp. 901-912

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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. 
@article{MZM_1973_14_6_a15,
     author = {N. S. Landkof},
     title = {Some remarks on stable stochastic processes and $\alpha$-superharmonic functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {901--912},
     publisher = {mathdoc},
     volume = {14},
     number = {6},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_14_6_a15/}
}
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N. S. Landkof. Some remarks on stable stochastic processes and $\alpha$-superharmonic functions. Matematičeskie zametki, Tome 14 (1973) no. 6, pp. 901-912. http://geodesic.mathdoc.fr/item/MZM_1973_14_6_a15/