  The phenomenon of intermittency has been widely discussed in physics
literature. This paper provides a model of intermittency based on L\'evy driven
Ornstein-Uhlenbeck (OU) type processes. Discrete superpositions of these
processes can be constructed to incorporate non-Gaussian marginal distributions
and long or short range dependence. While the partial sums of finite
superpositions of OU type processes obey the central limit theorem, we show
that the partial sums of a large class of infinite long range dependent
superpositions are intermittent. We discuss the property of intermittency and
behavior of the cumulants for the superpositions of OU type processes.
