Infinite divisibility of sub-stable processes. Part I. geometry of sub-spaces of L[alpha]-space

Jolanta K. Misiewicz

Stochastic Processes and their Applications, 1995, vol. 56, issue 1, 101-116

Abstract: Generalizing the definition of sub-Gaussian processes we define a sub-stable process as a scale mixture of symmetric stable processes and study its infinite divisibility. This turns out to be strictly dependent on the geometry of a sub-space () of the L[alpha]-space generated by the corresponding stable process. This space plays a similar role as the reproducing kernel Hilbert space in the case of sub-Gaussian processes. We also investigate the uniqueness of the representation and some related questions in the language of geometrical properties of this space.

Keywords: Stable processes Sub-stable processes Infinite divisibility; L[alpha]-spaces Spaces containing ln[alpha]'s uniformly (search for similar items in EconPapers)
Date: 1995
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