Random integral representation of operator-semi-self-similar processes with independent increments

Peter Becker-Kern

Stochastic Processes and their Applications, 2004, vol. 109, issue 2, 327-344

Abstract: 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.

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 (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (4)

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