Abstract :
We present a method for approximating the invariant measure of a randomly
perturbed mapping S of Rd. Cases where the unperturbed mapping is singular are
considered, as are cases where the sizes of random jumps are unbounded. Existence
of an invariant measure and convergence of the scheme are proved when the
mapping has strong contraction properties. The implementation is designed to be
useful in experimental situations where the map is known only approximately and
the distribution of the noise is unknown. Under the same contraction conditions,
we also prove that the invariant measure, the stationary measure of the associated
Markov chain, is approached exponentially under iteration of the perturbed map,
independent of the starting point.
