Abstract
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 ∈, 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 δ in space polynomial in log 1/∈ + log log 1/δ. 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 × n)-matrix to an exponentially large power in space polylogarithmic in n. Bibliography: 25 titles.
Original language | English (US) |
---|---|
Pages (from-to) | 1758-1783 |
Number of pages | 26 |
Journal | Sbornik Mathematics |
Volume | 208 |
Issue number | 12 |
DOIs | |
State | Published - 2017 |
All Science Journal Classification (ASJC) codes
- Mathematics (miscellaneous)
Keywords
- dynamical systems
- space-bounded computations