  SupOU processes can satisfy limit theorems while also exhibiting an unusual
growth of moments. This unusual growth, which is measured using the scaling
function, is referred to as "intermittency". For ordinary processes the growth
is associated to only one scale and therefore there is no intermittency. SupOU
processes, however, can be intermittent displaying a multiscale behavior. To
analyze these scales we focus on limit theorems, large deviation principles and
pathwise asymptotics as in the law of iterated logarithm.
