  We analyze dynamical systems subjected to an additive noise and their
deterministic limit. In this work, we will introduce a notion by which a
stochastic system has something like a Markov partition for deterministic
systems. For a chosen class of the noise profiles the Frobenius-Perron operator
associated to the noisy system is exactly represented by a stochastic
transition matrix of a finite size K. This feature allows us to introduce for
these stochastic systems a basis--Markov partition, defined herein,
irrespectively of whether the deterministic system possesses a Markov partition
or not. We show that in the deterministic limit, corresponding to K -->
infinity, the sequence of invariant measures of the noisy systems tends, in the
weak sense, to the invariant measure of the deterministic system. Thus by
introducing a small additive noise one may approximate transition matrices and
invariant measures of deterministic dynamical systems.
