Jose F. Alves, Vitor Araujo
Random perturbations of non-uniformly expanding 
maps
(460K, postscript)

ABSTRACT.  We give both sufficient conditions and 
necessary conditions for the stochastic stability of 
non-uniformly expanding maps either with or without 
critical sets. We also show that the number of probability 
measures describing the statistical asymptotic behaviour of 
random orbits is bounded by the number of SRB measures if 
the noise level is small enough. 
 As an application 
of these results we prove the stochastic stability of certain 
classes of non-uniformly expanding maps introduced in 
\cite{V} and \cite{ABV}.