Exponential law for random subshifts of finite type

Rousseau, Jérôme Le; Saussol, Benôıt; Varandas, Paulo

doi:10.1016/j.spa.2014.04.016

Cited by 14 publications

(25 citation statements)

References 46 publications

(63 reference statements)

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“…Remark 9. One can observe that this result is complementary to the ones proved in [27]. Indeed, in our result only the point x 0 is fixed and we proved an exponential law with respect to the invariant measure µ.…”

Section: Hitting Time Statistics For Random Dynamical Systemssupporting

confidence: 82%

“…Following this remark, random return times for dynamical systems were defined in [22] and the random recurrence rates were linked to the local dimension of the stationary measure. Recently, a few works on this theme are emerging, indeed, random hitting time indicators are studied in [4], [5] linked the distribution of hitting time for randomly perturbed dynamical systems and extreme value laws, and an exponential distribution for hitting time is proved in [27] for random subshift of finite type.…”

Section: Hitting Time Statistics For Random Dynamical Systemsmentioning

confidence: 99%

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Hitting time statistics for observations of dynamical systems

Rousseau

2014

Nonlinearity

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In this paper we study the distribution of hitting and return times for observations of dynamical systems. We apply this results to get an exponential law for the distribution of hitting and return times for rapidly mixing random dynamical systems. In particular, it allows us to obtain an exponential law for random expanding maps, random circle maps expanding in average and randomly perturbed dynamical systems.

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Section: Hitting Time Statistics For Random Dynamical Systemssupporting

confidence: 82%

Section: Hitting Time Statistics For Random Dynamical Systemsmentioning

confidence: 99%

Hitting time statistics for observations of dynamical systems

Rousseau

2014

Nonlinearity

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“…Random subshifts. We consider the random subshifts studied in [RSV14] and [RT15], in the setting of Hitting Times. Here we will keep using an Extreme Values approach and the statements can be seen as a translation of the corresponding results in [RSV14,RT15], in light of the connection between HTS and EVL proved in [FFT10,FFT11].…”

Section: Random Fibered Dynamical Systemsmentioning

confidence: 99%

Extreme Value Laws for non stationary processes generated by sequential and random dynamical systems

Freitas¹,

Freitas²,

Vaienti³

2017

Ann. Inst. H. Poincaré Probab. Statist.

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We develop and generalize the theory of extreme value for non-stationary stochastic processes, mostly by weakening the uniform mixing condition that was previously used in this setting. We apply our results to non-autonomous dynamical systems, in particular to sequential dynamical systems, both given by uniformly expanding maps and by maps with a neutral fixed point, and to a few classes of random dynamical systems. Some examples are presented and worked out in detail. Contents 1. Introduction 1.1. The motivation and the dynamical setting 1.2. Extreme Value Laws for general non-stationary processes 2. A general result for extreme value laws for non-stationary processes 2.1. Preliminaries to the argument 2.2. The construction of the blocks 2.3. Final argument 3. Sequential Dynamical Systems 3.1. General presentation 3.2. Stochastic processes for sequential systems 3.3. Examples 4. EVT for the sequential systems: an example of uniformly expanding map 4.1. EVT for the β-transformation

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“…Furthermore, they also proved that the same result holds for Markov chains, but with p being the largest eigenvalue of the matrix [(p ij ) 2 ], where [p ij ] is the transition matrix. This result was recently generalized in [15] for α-mixing processes with exponential decay and ψ-mixing processes with polynomial decay with a limit depending on the Rényi entropy of P and in [35] for random sequences in random environment. We recall that weak convergence theorems for sequence matching where also investigated over the last years (e.g [30,32]).…”

Section: Introductionmentioning

confidence: 93%

Matching strings in encoded sequences

Coutinho¹,

Lambert²,

Rousseau³

2020

Bernoulli

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We investigate the length of the longest common substring for encoded sequences and its asymptotic behaviour. The main result is a strong law of large numbers for a re-scaled version of this quantity, which presents an explicit relation with the Rényi entropy of the source. We apply this result to the zero-inflated contamination model and the stochastic scrabble. In the case of dynamical systems, this problem is equivalent to the shortest distance between two observed orbits and its limiting relationship with the correlation dimension of the pushforward measure. An extension to the shortest distance between orbits for random dynamical systems is also provided.keywords: string matching, Rényi entropy, shortest distance, correlation dimension, random dynamical systems, coding MSC: 60F15, 60Axx, 60C05, 37A50, 37A25, 37Hxx, 37C45, 94A17, 68P30

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Exponential law for random subshifts of finite type

Cited by 14 publications

References 46 publications

Hitting time statistics for observations of dynamical systems

Hitting time statistics for observations of dynamical systems

Extreme Value Laws for non stationary processes generated by sequential and random dynamical systems

Matching strings in encoded sequences

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