Tight space-noise tradeoffs in computing the ergodic measure

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 $δ$ in space polynomial in $\log 1/\varepsilon+\log\log 1/δ$. We also show that this b...