Convergence of iterates of a transfer operator, application to dynamical systems and to Markov chains
Jean-Pierre Conze; Albert Raugi
ESAIM: Probability and Statistics (2010)
- Volume: 7, page 115-146
- ISSN: 1292-8100
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topConze, Jean-Pierre, and Raugi, Albert. "Convergence of iterates of a transfer operator, application to dynamical systems and to Markov chains." ESAIM: Probability and Statistics 7 (2010): 115-146. <http://eudml.org/doc/104299>.
@article{Conze2010,
abstract = { We present a spectral theory for a class of
operators satisfying a weak
“Doeblin–Fortet" condition and apply it to a class of transition operators.
This gives the convergence of the series ∑k≥0krPkƒ,
$r \in \mathbb\{N\}$,
under some regularity assumptions and implies the central limit theorem
with a rate in $n^\{- \frac\{1\}\{2\} \}$ for the corresponding Markov chain.
An application to a non uniformly hyperbolic transformation on the
interval is also given.
},
author = {Conze, Jean-Pierre, Raugi, Albert},
journal = {ESAIM: Probability and Statistics},
keywords = {Transfer operator; convergence of iterates; Markov chains;
rate in the TCL
for dynamical systems; Borel-Cantelli property; non uniformly hyperbolic map.; transfer operator; rate in the TCL for dynamical systems; non uniformly hyperbolic map},
language = {eng},
month = {3},
pages = {115-146},
publisher = {EDP Sciences},
title = {Convergence of iterates of a transfer operator, application to dynamical systems and to Markov chains},
url = {http://eudml.org/doc/104299},
volume = {7},
year = {2010},
}
TY - JOUR
AU - Conze, Jean-Pierre
AU - Raugi, Albert
TI - Convergence of iterates of a transfer operator, application to dynamical systems and to Markov chains
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 7
SP - 115
EP - 146
AB - We present a spectral theory for a class of
operators satisfying a weak
“Doeblin–Fortet" condition and apply it to a class of transition operators.
This gives the convergence of the series ∑k≥0krPkƒ,
$r \in \mathbb{N}$,
under some regularity assumptions and implies the central limit theorem
with a rate in $n^{- \frac{1}{2} }$ for the corresponding Markov chain.
An application to a non uniformly hyperbolic transformation on the
interval is also given.
LA - eng
KW - Transfer operator; convergence of iterates; Markov chains;
rate in the TCL
for dynamical systems; Borel-Cantelli property; non uniformly hyperbolic map.; transfer operator; rate in the TCL for dynamical systems; non uniformly hyperbolic map
UR - http://eudml.org/doc/104299
ER -
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