极限定理中的间歇性和多尺度性
Intermittency and multiscaling in limit theorems
摘要：
最近发现，某些随机过程虽然具有不规则性，即矩的不寻常增长，但仍可能满足极限定理。在本文中，我们提供了这些复杂的限制现象的更深入的理解。我们表明，间歇性过程可能会表现出多尺度行为，涉及以不同的速度增长。这些比率对应不同的尺度。间歇性过程除了具有主导尺度外，还可能具有次级尺度。这些尺度的概率作为时间的幂函数下降到零。为了分析，我们考虑过程的增长率的大偏差。我们的方法是相当普遍的，涵盖了不同的可能情况，特别关注所谓的供应过程。
英文摘要：
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.
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