  The distribution of recurrence times or return intervals between extreme
events is important to characterize and understand the behavior of physical
systems and phenomena in many disciplines. It is well known that many physical
processes in nature and society display long range correlations. Hence, in the
last few years, considerable research effort has been directed towards studying
the distribution of return intervals for long range correlated time series.
Based on numerical simulations, it was shown that the return interval
distributions are of stretched exponential type. In this paper, we obtain an
analytical expression for the distribution of return intervals in long range
correlated time series which holds good when the average return intervals are
large. We show that the distribution is actually a product of power law and a
stretched exponential form. We also discuss the regimes of validity and perform
detailed studies on how the return interval distribution depends on the
threshold used to define extreme events.
