A regularity condition and a limit theorem for Harris ergodic Markov chains

Let (Xn)n≥0 be a Harris ergodic Markov chain and f be a real function on its state space. Consider the block sums ζ(i) for f ,i≥1, between consecutive visits to the atom given by the splitting technique of Nummelin. A regularity condition on the invariant probability measure π and a drift property a...

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Detalles Bibliográficos
Autor principal: Samur, Jorge Donato
Formato: Articulo
Lenguaje:Inglés
Publicado: 2004
Materias:
Ciencias Exactas
Almost sure invariance principle
Drift condition
Ergodicity of degree 2
f-regularity
Functional central limit theorem
Strong mixing
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/83391
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-83391
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Ciencias Exactas
Almost sure invariance principle
Drift condition
Ergodicity of degree 2
f-regularity
Functional central limit theorem
Strong mixing
spellingShingle Ciencias Exactas
Almost sure invariance principle
Drift condition
Ergodicity of degree 2
f-regularity
Functional central limit theorem
Strong mixing
Samur, Jorge Donato
A regularity condition and a limit theorem for Harris ergodic Markov chains
topic_facet Ciencias Exactas
Almost sure invariance principle
Drift condition
Ergodicity of degree 2
f-regularity
Functional central limit theorem
Strong mixing
description Let (Xn)n≥0 be a Harris ergodic Markov chain and f be a real function on its state space. Consider the block sums ζ(i) for f ,i≥1, between consecutive visits to the atom given by the splitting technique of Nummelin. A regularity condition on the invariant probability measure π and a drift property are introduced and proven to characterize the finiteness of the third moment of ζ(i). This is applied to obtain versions of an almost sure invariance principle for the partial sums of (f(Xn)), which is moreover given in the general case, due to Philipp and Stout for the countable state space case and to Csáki and Csörgo when the chain is strongly aperiodic. Conditions on the strong mixing coefficients are considered. A drift property equivalent to the finiteness of the second moment of ζ(i) is also given and applied to the functional central limit theorem.
format Articulo
Articulo
author Samur, Jorge Donato
author_facet Samur, Jorge Donato
author_sort Samur, Jorge Donato
title A regularity condition and a limit theorem for Harris ergodic Markov chains
title_short A regularity condition and a limit theorem for Harris ergodic Markov chains
title_full A regularity condition and a limit theorem for Harris ergodic Markov chains
title_fullStr A regularity condition and a limit theorem for Harris ergodic Markov chains
title_full_unstemmed A regularity condition and a limit theorem for Harris ergodic Markov chains
title_sort regularity condition and a limit theorem for harris ergodic markov chains
publishDate 2004
url http://sedici.unlp.edu.ar/handle/10915/83391
work_keys_str_mv AT samurjorgedonato aregularityconditionandalimittheoremforharrisergodicmarkovchains
AT samurjorgedonato regularityconditionandalimittheoremforharrisergodicmarkovchains
bdutipo_str Repositorios
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