  A well-known stochastic model for intermittent fluctuations in physical
systems is investigated. The model is given by a super-position of uncorrelated
exponential pulses, and the degree of pulse overlap is interpreted as an
intermittency parameter. Expressions for excess time statistics, that is, the
rate of level crossings above a given threshold and the average time spent
above the threshold, are derived from the joint distribution of the process and
its derivative. Limits of both high and low intermittency are investigated and
compared to previously known results. In the case of a strongly intermittent
process, the distribution of times spent above threshold is obtained
analytically. This expression is verified numerically, and the distribution of
times above threshold is explored for other intermittency regimes. The
numerical results compare favorably to known results for the distribution of
times above the mean threshold for an Ornstein-Uhlenbeck process. This
contribution generalizes the excess time statistics for the stochastic model
which find applications in a wide diversity of natural and technological
systems.
