Geodesic
Superposition of Ornstein–Uhlenbeck type processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 45 (2000) no. 2, pp. 289-311 Cet article a éte moissonné depuis la source Math-Net.Ru

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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, cumulative processes, self-similarity.
Mots-clés : Lévy processes, superpositions 
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     author = {O. E. Barndorff-Nielsen},
     title = {Superposition of {Ornstein{\textendash}Uhlenbeck} type processes},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {289--311},
     year = {2000},
     volume = {45},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_2000_45_2_a4/}
}
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O. E. Barndorff-Nielsen. Superposition of Ornstein–Uhlenbeck type processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 45 (2000) no. 2, pp. 289-311. http://geodesic.mathdoc.fr/item/TVP_2000_45_2_a4/