Return-Time Statistics, Hitting-Time Statistics and Inducing

2014 ◽  
pp. 217-227 ◽  
Author(s):  
Nicolai T. A. Haydn ◽  
Nicole Winterberg ◽  
Roland Zweimüller
Keyword(s):  
Return Time ◽  
Hitting Time ◽  
Return Time Statistics

scholarly journals RETURN TIME STATISTICS OF INVARIANT MEASURES FOR INTERVAL MAPS WITH POSITIVE LYAPUNOV EXPONENT

2009 ◽  
Vol 09 (01) ◽  
pp. 81-100 ◽  
Author(s):  
HENK BRUIN ◽  
MIKE TODD
Keyword(s):  
Lyapunov Exponent ◽  
Invariant Measures ◽  
Return Time ◽  
Continuous Invariant Measure ◽  
Absolutely Continuous ◽  
Interval Maps ◽  
Absolutely Continuous Invariant Measure ◽  
Normal Fluctuations ◽  
Return Time Statistics ◽  
Absolutely Continuous Invariant

We prove that multimodal maps with an absolutely continuous invariant measure have exponential return time statistics around almost every point. We also show a "polynomial Gibbs property" for these systems, and that the convergence to the entropy in the Ornstein–Weiss formula has normal fluctuations. These results are also proved for equilibrium states of some Hölder potentials.

scholarly journals Return time statistics via inducing

2003 ◽  
Vol 23 (4) ◽  
pp. 991-1013 ◽  
Author(s):  
H. BRUIN ◽  
B. SAUSSOL ◽  
S. TROUBETZKOY ◽  
S. VAIENTI
Keyword(s):  
Return Time ◽  
Return Time Statistics

Correlation decay and return time statistics

1999 ◽  
Vol 131 (1-4) ◽  
pp. 68-77 ◽  
Author(s):  
Roberto Artuso
Keyword(s):  
Return Time ◽  
Correlation Decay ◽  
Return Time Statistics

scholarly journals Extreme value theory and return time statistics for dispersing billiard maps and flows, Lozi maps and Lorenz-like maps

2011 ◽  
Vol 31 (5) ◽  
pp. 1363-1390 ◽  
Author(s):  
CHINMAYA GUPTA ◽  
MARK HOLLAND ◽  
MATTHEW NICOL
Keyword(s):  
Time Series ◽  
Hyperbolic Systems ◽  
Return Time ◽  
Value Theory ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Distributed Processes ◽  
Return Time Statistics ◽  
Generic Points ◽  
Lozi Maps

AbstractIn this paper we establish extreme value statistics for observations on a class of hyperbolic systems: planar dispersing billiard maps and flows, Lozi maps and Lorenz-like maps. In particular, we show that for time series arising from Hölder observations on these systems which are maximized at generic points the successive maxima of the time series are distributed according to the corresponding extreme value distributions for independent identically distributed processes. These results imply an exponential law for the hitting and return time statistics of these dynamical systems.

scholarly journals Return time statistics for unimodal maps

2003 ◽  
Vol 176 (1) ◽  
pp. 77-94 ◽  
Author(s):  
H. Bruin ◽  
S. Vaienti
Keyword(s):  
Return Time ◽  
Unimodal Maps ◽  
Return Time Statistics

scholarly journals Multifractal Properties of Return Time Statistics

2002 ◽  
Vol 88 (22) ◽  
Author(s):  
Nicolai Hadyn ◽  
José Luevano ◽  
Giorgio Mantica ◽  
Sandro Vaienti
Keyword(s):  
Return Time ◽  
Return Time Statistics

scholarly journals Fluctuations Analysis of Finite Discrete Birth and Death Chains with Emphasis on Moran Models with Mutations

2013 ◽  
Vol 2013 ◽  
pp. 1-21 ◽  
Author(s):  
Thierry E. Huillet
Keyword(s):  
Equilibrium State ◽  
Large Population ◽  
Return Time ◽  
Hitting Time ◽  
Point Of View ◽  
First Hitting Time ◽  
Total Size ◽  
Cutoff Phenomenon ◽  
Moran Model ◽  
First Return Time

The Moran model is a discrete-time birth and death Markov chain describing the evolution of the number of type 1 alleles in a haploid population with two alleles whose total size N is preserved during the course of evolution. Bias mechanisms such as mutations or selection can affect its neutral dynamics. For the ergodic Moran model with mutations, we get interested in the fixation probabilities of a mutant, the growth rate of fluctuations, the first hitting time of the equilibrium state starting from state {0}, the first return time to the equilibrium state, and the first hitting time of {N} starting from {0}, together with the time needed for the walker to reach its invariant measure, again starting from {0}. For the last point, an appeal to the notion of Siegmund duality is necessary, and a cutoff phenomenon will be made explicit. We are interested in these problems in the large population size limit N→∞. The Moran model with mutations includes the heat exchange models of Ehrenfest and Bernoulli-Laplace as particular cases; these were studied from the point of view of the controversy concerning irreversibility (H-theorem) and the recurrence of states.

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