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On weighted tempered moving averages processes. (English) Zbl 1152.60326

Summary: We introduce a new class of processes: the weighted tempered moving averages processes, which include the tempered moving averages processes as a particular case. They generalize the class of tempered moving averages process which is widely known and has many applications. In some cases they share with the tempered Lévy process the following property: in a close time-frame they behave like an \(\alpha\)-stable process while in a long time frame like a gaussian process. Additionally we prove that under certain conditions they are mixing and hence ergodic.

MSC:

60G52 Stable stochastic processes
60E07 Infinitely divisible distributions; stable distributions
60H05 Stochastic integrals
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[1] DOI: 10.1016/j.spa.2006.10.003 · Zbl 1118.60037 · doi:10.1016/j.spa.2006.10.003
[2] DOI: 10.1016/j.spa.2006.01.008 · Zbl 1102.60036 · doi:10.1016/j.spa.2006.01.008
[3] DOI: 10.1016/0047-259X(82)90073-2 · Zbl 0493.60046 · doi:10.1016/0047-259X(82)90073-2
[4] Pérez J.L., Preprint, Instituto de Matemáticas, Universidad Nacional Autónoma de México 836 pp 1– (2007)
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