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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.

DOI: https://doi.org/10.4213/tvp464

Full text: PDF file (942 kB)

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

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Received: 04.03.1999
Language:

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
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\jour Theory Probab. Appl.
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    4. Nicolato E., Venardos E., “Option pricing in stochastic volatility models of the Ornstein–Uhlenbeck type”, Mathematical Finance, 13:4 (2003), 445–466  crossref  mathscinet  zmath  isi  scopus
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    12. von Asmuth J.R., Bierkens M.F.P., “Modeling irregularly spaced residual series as a continuous stochastic process”, Water Resources Research, 41:12 (2005), W12404  crossref  adsnasa  isi  scopus
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    16. Theory Probab. Appl., 50:1 (2006), 1–15  mathnet  crossref  mathscinet  zmath  isi  elib
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    21. Kluppelberg C., Lindner A., Maller R., “Continuous time volatility modelling: COGARCH versus Ornstein–Uhlenbeck models”, From Stochastic Calculus to Mathematical Finance: The Shiryaev Festschrift, 2006, 393–419  crossref  mathscinet  zmath  isi
    22. Fasen V., Klueppelberg C., “Extremes of supOU processes”, Stochastic Analysis and Applications, Abel Symposia, 2, 2007, 339–359  crossref  mathscinet  zmath  isi
    23. O. V. Rusakov, “Sums of independent Poisson subordinators and their connections with strictly $\alpha$-stable processes of the Ornstein–Uhlenbeck type”, J. Math. Sci. (N. Y.), 159:3 (2009), 350–357  mathnet  crossref  zmath
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