357 research outputs found
Almost Sure Invariance Principle For Nonuniformly Hyperbolic Systems
We prove an almost sure invariance principle that is valid for general
classes of nonuniformly expanding and nonuniformly hyperbolic dynamical
systems. Discrete time systems and flows are covered by this result. In
particular, the result applies to the planar periodic Lorentz flow with finite
horizon. Statistical limit laws such as the central limit theorem, the law of
the iterated logarithm, and their functional versions, are immediate
consequences.Comment: 21 pages, To appear in Communications in Mathematical Physic
Annealed and quenched limit theorems for random expanding dynamical systems
In this paper, we investigate annealed and quenched limit theorems for random
expanding dynamical systems. Making use of functional analytic techniques and
more probabilistic arguments with martingales, we prove annealed versions of a
central limit theorem, a large deviation principle, a local limit theorem, and
an almost sure invariance principle. We also discuss the quenched central limit
theorem, dynamical Borel-Cantelli lemmas, Erd\"os-R\'enyi laws and
concentration inequalities.Comment: Appeared online in Probability Theory and Related Field
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