积分有限方差supOU过程的极限定理、矩的标度和矩的不变性
Limit theorems, scaling of moments and intermittency for integrated finite variance supOU processes
摘要：
叠加的Ornstein-Uhlenbeck型（supplementary）过程提供了丰富的平稳随机过程，其边缘分布和相关结构可以独立建模。我们表明，他们也可以显示不稳定性，影响增长率的时刻的现象。为此，我们研究了具有有限方差的集成供应过程的极限行为。在适当的归一化之后，根据相关函数的衰减和边缘分布的特征三元组，可能出现四种不同的限制过程。为了表明，supplementary过程可能会表现出不稳定性，我们建立的增长率的时刻的四个限制的情况下。速率的变化表明存在着不稳定性，在这里用绝对矩的渐近行为的变点来表示。
英文摘要：
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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