Semi-Selfsimilar Processes

Makoto Maejima () and Ken-iti Sato
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Makoto Maejima: Keio University

Journal of Theoretical Probability, 1999, vol. 12, issue 2, 347-373

Abstract: Abstract A notion of semi-selfsimilarity of R d -valued stochastic processes is introduced as a natural extension of the selfsimilarity. Several topics on semi-selfsimilar processes are studied: the existence of the exponent for semi-selfsimilar processes; characterization of semi-selfsimilar processes as scaling limits; relationship between semi-selfsimilar processes with independent increments and semi-selfdecomposable distributions, and examples; construction of semi-selfsimilar processes with stationary increments; and extension of the Lamperti transformation. Semi-stable processes where all joint distributions are multivariate semi-stable are also discussed in connection with semi-selfsimilar processes. A wide-sense semi-selfsimilarity is defined and shown to be reducible to semi-selfsimilarity.

Keywords: Selfsimilar process; semi-selfsimilar process; semi-stable process; Lévy process (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (7)

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DOI: 10.1023/A:1021621926463

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