Speaker
Description
Superpositions of Ornstein-Uhlenbeck type processes (supOU) provide a rich class of stationary stochastic processes for which the marginal distribution and the dependence structure may be modeled independently. Limit theorems will be presented both for the finite and infinite variance integrated supOU processes. Moreover, it will be shown that integrated supOU processes may exhibit a phenomenon of intermittency meaning that their higher order moments grow faster than it would be expected from the limit theorems. We will then discuss how intermittency affects the limiting behavior of the process through large deviations theory. We also present the results on the almost sure rate of growth and the law of iterated logarithm type results for certain cases. Even though the growth of moments may suggest differently, the almost sure growth is of the same order as in the weak limit theorems.
