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

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  • Misiewicz, Jolanta K.

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.

Suggested Citation

  • Misiewicz, Jolanta K., 1995. "Infinite divisibility of sub-stable processes. Part I. geometry of sub-spaces of L[alpha]-space," Stochastic Processes and their Applications, Elsevier, vol. 56(1), pages 101-116, March.
    • Handle: RePEc:eee:spapps:v:56:y:1995:i:1:p:101-116
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    References listed on IDEAS

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    1. de Araujo, Aloisio Pessoa, 1978. "On the central limit theorem in Banach spaces," Journal of Multivariate Analysis, Elsevier, vol. 8(4), pages 598-613, December.
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