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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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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DOI: https://doi.org/10.1007/BF01192553
Keywords
- Probability Density
- Stochastic Process
- Probability Theory
- High Dimension
- Invariant Measure