  In this note we obtain tight bounds on the space-complexity of computing the
ergodic measure of a low-dimensional discrete-time dynamical system affected by
Gaussian noise. If the scale of the noise is $\varepsilon$, and the function
describing the evolution of the system is not by itself a source of
computational complexity, then the density function of the ergodic measure can
be approximated within precision $\delta$ in space polynomial in $\log
1/\varepsilon+\log\log 1/\delta$. We also show that this bound is tight up to
polynomial factors.
  In the course of showing the above, we prove a result of independent interest
in space-bounded computation: that it is possible to exponentiate an $n$ by $n$
matrix to an exponentially large power in space polylogarithmic in $n$.
