Abstract
Employing a general theorem on large deviations together with Walters' result on uniqueness of equilibrium states for some mappings which expand distances I derive large deviation bounds for random expanding maps which involve the entropy similarly to large deviations for dynamical systems. Relativized large deviations are discussed, as well.
Keywords
- Markov Chain
- Lyapunov Exponent
- Invariant Measure
- Conditional Measure
- Topological Pressure
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References
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P. Walters, Invariant measures and equilibrium states for some mappings which expand distances, Trans. Amer. Math. Soc. 236, (1978), 121–153.
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© 1991 Springer-Verlag
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Kifer, Y. (1991). Large deviations for random expanding maps. In: Arnold, L., Crauel, H., Eckmann, JP. (eds) Lyapunov Exponents. Lecture Notes in Mathematics, vol 1486. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086667
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DOI: https://doi.org/10.1007/BFb0086667
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54662-7
Online ISBN: 978-3-540-46431-0
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