Limit theorems, scaling of moments and intermittency for integrated finite variance supOU processes

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.

Stochastic Processes and their Applications

References in corpus (3)

• Multivariate supOU processes
• Intermittency for the stochastic heat equation with Lévy noise
• The almost-sure asymptotic behavior of the solution to the stochastic heat equation with Lévy noise

Cited by in corpus (6)

• The almost-sure asymptotic behavior of the solution to the stochastic heat equation with Lévy noise
• Dickman type stochastic processes with short- and long- range dependence
• Intermittency and multiscaling in limit theorems
• Stochastic volatility model with long memory for water quantity-quality dynamics
• Intermittency in the small-time behavior of Lévy processes
• Weak dependence and GMM estimation of supOU and mixed moving average processes