Limit theorems,scaling of moments and intermittency for integrated finite variance supOU processes |
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Institution: | 1. Istituto per le Applicazioni del Calcolo, CNR, Roma, Italy;2. Dipartimento di Informatica, Università di Torino, Italy;3. Dipartimento di Elettronica, Politecnico di Torino, Italy;1. School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF244AG, UK;2. Department of Mathematics, J.J. Strossmayer University of Osijek, Trg Ljudevita Gaja 6, HR-31 000 Osijek, Croatia;3. Departments of Psychiatry and Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA |
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Abstract: | Superpositions of Ornstein–Uhlenbeck type (supOU) processes provide a rich class of stationary stochastic processes for which the marginal distribution and the dependence structure may be modeled independently. We show that they can also display intermittency, a phenomenon affecting the rate of growth of moments. To do so, we investigate the limiting behavior of integrated supOU processes with finite variance. After suitable normalization four different limiting processes may arise depending on the decay of the correlation function and on the characteristic triplet of the marginal distribution. To show that supOU processes may exhibit intermittency, we establish the rate of growth of moments for each of the four limiting scenarios. The rate change indicates that there is intermittency, which is expressed here as a change-point in the asymptotic behavior of the absolute moments. |
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Keywords: | SupOU processes Limit theorems Intermittency |
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