Markov approximation of chains of infinite order in the d̄-metric

S. Gallo; M. Lerasle; D. Y. Takahashi

Markov approximation of chains of infinite order in the d̄-metric

S. Gallo, M. Lerasle, D. Y. Takahashi

Research output: Contribution to journal › Article › peer-review

Abstract

We obtaiu explicit upper bounds for the d̄-distance between a chain of infinite order and its canonical k-steps Markov approximation. Our proof is entirely constructive and involves a "coupling from the past" argument. The new method covers non-necessarily continuous probability kernels, and chains with null transition probabilities. These results imply in particular the Bernoulli property for these processes.

Original language	English
Pages (from-to)	51-82
Number of pages	32
Journal	Markov Processes and Related Fields
Volume	19
Issue number	1
Publication status	Published - 3 Jun 2013
Externally published	Yes

Keywords

Canonical Markov approximation
Chains of infinite order
Coupling from the past algorithms
D̄-distance

Cite this

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title = "Markov approximation of chains of infinite order in the {\=d}-metric",

abstract = "We obtaiu explicit upper bounds for the {\=d}-distance between a chain of infinite order and its canonical k-steps Markov approximation. Our proof is entirely constructive and involves a {"}coupling from the past{"} argument. The new method covers non-necessarily continuous probability kernels, and chains with null transition probabilities. These results imply in particular the Bernoulli property for these processes.",

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year = "2013",

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T1 - Markov approximation of chains of infinite order in the d̄-metric

AU - Gallo, S.

AU - Lerasle, M.

AU - Takahashi, D. Y.

PY - 2013/6/3

Y1 - 2013/6/3

N2 - We obtaiu explicit upper bounds for the d̄-distance between a chain of infinite order and its canonical k-steps Markov approximation. Our proof is entirely constructive and involves a "coupling from the past" argument. The new method covers non-necessarily continuous probability kernels, and chains with null transition probabilities. These results imply in particular the Bernoulli property for these processes.

AB - We obtaiu explicit upper bounds for the d̄-distance between a chain of infinite order and its canonical k-steps Markov approximation. Our proof is entirely constructive and involves a "coupling from the past" argument. The new method covers non-necessarily continuous probability kernels, and chains with null transition probabilities. These results imply in particular the Bernoulli property for these processes.

KW - Canonical Markov approximation

KW - Chains of infinite order

KW - Coupling from the past algorithms

KW - D̄-distance

M3 - Article

AN - SCOPUS:84878290693

SN - 1024-2953

VL - 19

SP - 51

EP - 82

JO - Markov Processes and Related Fields

JF - Markov Processes and Related Fields

IS - 1

ER -

Markov approximation of chains of infinite order in the d̄-metric

Abstract

Keywords

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