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Intermittency And Multiscaling In Limit Theorems

Author

Listed:
  • DANIJEL GRAHOVAC

    (Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, 31000 Osijek, Croatia)

  • NIKOLAI N. LEONENKO

    (��School of Mathematics, Cardiff University, Senghennydd Road, Cardiff, Wales CF24 4AG, UK)

  • MURAD S. TAQQU

    (��Department of Mathematics and Statistics, Boston University, Boston, MA 02215, USA)

Abstract

It has been recently discovered that some random processes may satisfy limit theorems even though they exhibit intermittency, namely an unusual growth of moments. In this paper, we provide a deeper understanding of these intricate limiting phenomena. We show that intermittent processes may exhibit a multiscale behavior involving growth at different rates. To these rates correspond different scales. In addition to a dominant scale, intermittent processes may exhibit secondary scales. The probability of these scales decreases to zero as a power function of time. For the analysis, we consider large deviations of the rate of growth of the processes. Our approach is quite general and covers different possible scenarios with special focus on the so-called supOU processes.

Suggested Citation

  • Danijel Grahovac & Nikolai N. Leonenko & Murad S. Taqqu, 2022. "Intermittency And Multiscaling In Limit Theorems," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(07), pages 1-18, November.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:07:n:s0218348x22501377
    DOI: 10.1142/S0218348X22501377
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