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Characterization of stable processes by identically distributed stochastic integrals

Published online by Cambridge University Press:  01 July 2016

M. Riedel
M. Riedel*
Affiliation:
Karl-Marx-Universität Leipzig
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Abstract

Let X(t) be a homogeneous and continuous stochastic process with independent increments. The subject of this paper is to characterize the stable process by two identically distributed stochastic integrals formed by means of X(t) (in the sense of convergence in probability). The proof of the main results is based on a modern extension of the Phragmén-Lindelöf theory.

Keywords

WIENER PROCESSINFINITELY DIVISIBLE DISTRIBUTIONLÉVY CANONICAL REPRESENTATIONCONTINUOUSHOMOGENEOUS PROCESS WITH INDEPENDENT INCREMENTSPHRAGMÉN-LINDELÖF THEORY
Type
Research Article
Information
Advances in Applied Probability , Volume 12 , Issue 3 , September 1980 , pp. 689 - 709
Copyright
Copyright © Applied Probability Trust 1980 

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