Authors
Advisor(s)
Abstract(s)
This thesis addresses the statistical properties of dynamical systems that admit an
induced Weak Gibbs Markov map (not necessarily full branch). More precisely, it
provides estimates on the decay of correlations, a Central Limit Theorem and Large
Deviations results for such dynamical systems. These estimates for the decay of correlations
and the Central Limit Theorem are obtained for H¨older observables as well
as larger classes of observables with weaker regularity than H¨older. The results on
Large Deviations are a consequence of the estimates on the decay of correlations in
this thesis.
To deal with the estimates on the decay of correlations and the Central Limit Theorem
for H¨older observables, our approach generalizes L.-S. Young’s coupling arguments.
Initially, we discuss how to ensure that the invariant probability measure for the tower
system of an inducedWeak Gibbs Markov map, is mixing. Then, we estimate the decay
of correlations in terms of the tail of the return time function and derive the Central
Limit Theorem for the tower system. Finally, using a semiconjugacy, we obtain results
on the decay of correlations and Central Limit Theorem for H¨older observables.
The results for larger classes of observables follow a similar strategy. Specifically, we
extend the decay of correlation estimates, the Central Limit Theorem and the Large
Deviations estimates for H¨older observables to larger classes of observables.
Esta tese aborda propriedades estatísticas de sistemas dinâmicos que admitem uma transformação induzida Gibbs-Markov fraca (ou seja, sem a exigência de retornos completos). [...]
Esta tese aborda propriedades estatísticas de sistemas dinâmicos que admitem uma transformação induzida Gibbs-Markov fraca (ou seja, sem a exigência de retornos completos). [...]
Description
Keywords
Decaimento de correlações Grandes Desvios Teorema do Limite Central Torre de Young Transformação Gibbs-Markov fraca