Spectral representation of semistable processes, and semistable laws on Banach spaces
type: Item
instance of: scholarly article
title: Spectral representation of semistable processes, and semistable laws on Banach spaces
zbMATH Open document ID: 0621.60017
DOI: 10.1016/0047-259X(87)90103-5
author: Balram S. Rajput
author: Kavi Rama-Murthy
published in: Journal of Multivariate Analysis
publication date: 1987-01-01T00:00:00Z
review text: The spectral representation of symmetric stable processes are useful in studying sample path properties as well as prediction and estimation problems; cf. \textit{C. D. Hardin} jun., ibid. 12, 385-401 (1982; Zbl 0493.60046). In this paper the authors give a definition of stochastic integrals for a suitable class of functions relative to semistable and stable random measures. Moreover they obtain spectral representations for arbitrary (not necessarily symmetric) semistable and stable processes of index \(0<\alpha <2\), \(\alpha\neq 1.\) A condition for independence of infinitely divisible Banach-valued random variables, in terms of their Lévy measure, is given. As a consequence a criterion for independence of stochastic integrals is deduced. Reviewer's remark: The spectral representation theorem for general (i.e., possibly skewed or asymmetric) stable processes is also due to \textit{C. D. Hardin} jun., Univ. North Carolina, Center for Stochastic Processes, Technical Report {\#}79 (September 1984).
Mathematics Subject Classification ID: 60E07
Mathematics Subject Classification ID: 60B11
Mathematics Subject Classification ID: 60H05
zbMATH DE Number: 4007329
zbMATH Keywords: spectral representation of symmetric stable processes
zbMATH Keywords: sample path properties
zbMATH Keywords: semistable and stable processes
zbMATH Keywords: infinitely divisible Banach- valued random variables
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4007329