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Superposition of Ornstein–Uhlenbeck type processes

O. E. Barndorff-Nielsen

Institute of Mathematics, University of Aarhus, Denmark

Abstract: A class of superpositions of Ornstein–Uhlenbeck type processes is constructed in terms of integrals with respect to independently scattered random measures. Under specified conditions, the resulting processes exhibit long-range dependence. By integration, the superpositions yield cumulative processes with stationary increments, and integration with respect to processes of the latter type is defined. A limiting procedure results in processes that, in the case of square integrability, are second-order self-similar with stationary increments. Other resulting limiting processes are stable and self-similar with stationary increments.

Keywords: Ornstein–Uhlenbeck processes, Lévy processes, superpositions, cumulative processes, self-similarity.

Received: 04.03.1999

Language: English

DOI: 10.4213/tvp464

 English version: Theory of Probability and its Applications, 2001, 45:2, 175–194

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