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This article is cited in 157 scientific papers (total in 157 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.
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
Linking options:
https://www.mathnet.ru/eng/tvp464https://doi.org/10.4213/tvp464 https://www.mathnet.ru/eng/tvp/v45/i2/p289
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