INTERMITTENCY AND MULTISCALING IN LIMIT THEOREMS

doi:10.1142/S0218348X22501377

INTERMITTENCY AND MULTISCALING IN LIMIT THEOREMS

2022-09-29

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DOI：10.1142/S0218348X22501377

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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.

Keywords:

Intermittency

Multiscaling

Limit Theorems

Large Deviations

Convergence of Moments

INTERMITTENCY AND MULTISCALING IN LIMIT THEOREMS

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