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Large deviations in dynamical systems and stochastic processes. (English) Zbl 0714.60019

The paper presents a general large deviations result for families of random probability measures on a compact metric space \(X\). An upper large deviation bound is established provided the pressure of every continuous function on \(X\) exists; the rate functional is the convex conjugate of the pressure. A lower bound is more difficult to obtain. The lower bound is proved assuming that there exist a countable dense set of continuous functions on \(X\) such that all finite linear combinations of functions from this set have a unique equilibrium state.
Reviewer: H.Crauel

MSC:

60F10 Large deviations
37H99 Random dynamical systems
37D99 Dynamical systems with hyperbolic behavior
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