منابع مشابه
Large Deviation for Return times in Open Sets for Axiom a Diffeomorphisms
For axiom A diffeomorphisms and equilibrium state, we prove a Large deviation result for the sequence of successive return times into a fixed open set, under some assumption on the boundary. Our result relies on and extends the work by Chazottes and Leplaideur who where considering cylinder sets of a Markov partition.
متن کاملThe R’enyi Entropy Function and the Large Deviation of Short Return Times
We consider the Rényi entropy function for weakly ψ-mixing systems. The first main result proves existence and regularity properties. The second main result of the paper is to get the decay rate for the large deviation of the return time to cylinder sets. We show it to be exponential with a rate given by the Rényi entropy function. Finally we also obtain bounds for the free energy.
متن کاملLarge Deviation Estimates for Exceedance times of Perpetuity Sequences and Their Dual Processes1 by Dariusz Buraczewski∗,
In a variety of problems in pure and applied probability, it is relevant to study the large exceedance probabilities of the perpetuity sequence Yn := B1 + A1B2 + · · · + (A1 · · ·An−1)Bn, where (Ai,Bi) ⊂ (0,∞)× R. Estimates for the stationary tail distribution of {Yn} have been developed in the seminal papers of Kesten [Acta Math. 131 (1973) 207–248] and Goldie [Ann. Appl. Probab. 1 (1991) 126–...
متن کاملLarge deviation estimates for exceedance times of perpetuity sequences and their dual processes
In a variety of problems in pure and applied probability, it is of relevant to study the large exceedance probabilities of the perpetuity sequence Yn := B1 + A1B2 + · · · + (A1 · · ·An−1)Bn, where (Ai, Bi) ⊂ (0,∞) × R. Estimates for the stationary tail distribution of {Yn} have been developed in the seminal papers of Kesten (1973) and Goldie (1991). Specifically, it is well-known that if M := s...
متن کاملLarge Deviations for Return times in Non-rectangle Sets for Axiom a Diffeomorphisms
For Axiom A diffeomorphisms and equilibrium states, we prove a Large deviations result for the sequence of successive return times into a fixed Borel set, under some assumption on the boundary. Our result relies on and extends the work by Chazottes and Leplaideur who considered cylinder sets of a Markov partition.
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 2018
ISSN: 0951-7715,1361-6544
DOI: 10.1088/1361-6544/aadc03