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Teor. Veroyatnost. i Primenen., 2000, Volume 45, Issue 2, Pages 289–311 (Mi tvp464)  

This article is cited in 89 scientific papers (total in 89 papers)

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.


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

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Received: 04.03.1999

Citation: O. E. Barndorff-Nielsen, “Superposition of Ornstein–Uhlenbeck type processes”, Teor. Veroyatnost. i Primenen., 45:2 (2000), 289–311; Theory Probab. Appl., 45:2 (2001), 175–194

Citation in format AMSBIB
\by O.~E.~Barndorff-Nielsen
\paper Superposition of Ornstein--Uhlenbeck type processes
\jour Teor. Veroyatnost. i Primenen.
\yr 2000
\vol 45
\issue 2
\pages 289--311
\jour Theory Probab. Appl.
\yr 2001
\vol 45
\issue 2
\pages 175--194

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