This article is cited in 2 papers

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

N. S. Landkof

Rostov-on-Don State Building University

Abstract: 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.

UDC: 519.2

Received: 22.03.1971

 English version: Mathematical Notes, 1973, 14:6, 1078–1084

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