Tight space-noise tradeoffs in computing the ergodic measure

M. Braverman, C. Rojas, J. Schneider

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)1758-1783
Number of pages26
JournalSbornik Mathematics
Volume208
Issue number12
DOIs
StatePublished - Jan 1 2017

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Keywords

  • dynamical systems
  • space-bounded computations

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