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Ergodic properties of Markov maps inR d
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  • Published: December 1991

Ergodic properties of Markov maps inR d

  • Piotr Bugiel1 

Probability Theory and Related Fields volume 88, pages 483–496 (1991)Cite this article

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Summary

For domainsI⊂R d (bounded or not) the notion of a Markov map fromI into itself is developed. It is shown that under a condition of Rényi type and the assumption that the map ϕ is Markov, any probability density tends inL 1-norm to a unique invariant measure under the action of the Perron-Frobenius operatorP ϕ. The smoothness and ergodic properties of that invariant measure are studied. The paper generalizes results of Lasota and Yorke from dimension one to higher dimension.

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Authors and Affiliations

  1. Department of Mathematics, Jagellonian University, ul. Reymonta 4, PL-30-059, Kraków, Poland

    Piotr Bugiel

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  1. Piotr Bugiel
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Bugiel, P. Ergodic properties of Markov maps inR d . Probab. Th. Rel. Fields 88, 483–496 (1991). https://doi.org/10.1007/BF01192553

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  • Received: 25 April 1990

  • Revised: 01 December 1990

  • Issue Date: December 1991

  • DOI: https://doi.org/10.1007/BF01192553

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Keywords

  • Probability Density
  • Stochastic Process
  • Probability Theory
  • High Dimension
  • Invariant Measure
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