  This paper describes limiting behaviour of tail empirical process associated
with long memory stochastic volatility models. We show that such process has
dichotomous behaviour, according to an interplay between a Hurst parameter and
a tail index. In particular, the limit may be non-Gaussian and/or degenerate,
indicating an influence of long memory. On the other hand, tail empirical
process with random levels never suffers from long memory. This is very
desirable from a practical point of view, since such the process may be used to
construct Hill estimator of the tail index. To prove our results we need to
establish several new results for regularly varying distribution functions,
which may be of independent interest.
