Random integral representation of operator-semi-self-similar processes with independent increments
Jeanblanc et al. (Stochastic Process. Appl. 100 (2002) 223) give a representation of self-similar processes with independent increments by stochastic integrals with respect to background driving Lévy processes. Via Lamperti's transformation these processes correspond to stationary Ornstein-Uhlenbeck processes. In the present paper we generalize the integral representation to multivariate processes with independent increments having the weaker scaling property of operator-semi-self-similarity. It turns out that the corresponding background driving process has periodically stationary increments and in general is no longer a Lévy process. Just as well it turns out that the Lamperti transform of an operator-semi-self-similar process with independent increments defines a periodically stationary process of Ornstein-Uhlenbeck type.
Year of publication: |
2004
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Authors: | Becker-Kern, Peter |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 109.2004, 2, p. 327-344
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Publisher: |
Elsevier |
Keywords: | Operator-semi-self-similar process Operator-semi-self-decomposable distribution Semi-stable hemigroup Periodic stationarity Background driving process Generalized Ornstein-Uhlenbeck process Operator Lévy bridge |
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