Geodesic
Tight space-noise tradeoffs in computing the ergodic measure
Sbornik. Mathematics, Tome 208 (2017) no. 12, pp. 1758-1783

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In this paper 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 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: namely, that it is possible to exponentiate an $(n\times n)$-matrix to an exponentially large power in space polylogarithmic in $n$. Bibliography: 25 titles.
Keywords: dynamical systems, space-bounded computations. 
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     author = {M. Braverman and C. Rojas and J. Schneider},
     title = {Tight space-noise tradeoffs in computing the ergodic measure},
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M. Braverman; C. Rojas; J. Schneider. Tight space-noise tradeoffs in computing the ergodic measure. Sbornik. Mathematics, Tome 208 (2017) no. 12, pp. 1758-1783. http://geodesic.mathdoc.fr/item/SM_2017_208_12_a2/