Finite-state, stationary, ø-mixing processes which are not very weak Bernoulli with rate O(1/n)

Robert M. Burton; Manfred Denker; Doris Fiebig

doi:10.1016/0304-4149(94)90151-1

Finite-state, stationary, ø-mixing processes which are not very weak Bernoulli with rate O(1/n)

Robert M. Burton, Manfred Denker, Doris Fiebig

Mathematics

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

Abstract

In this paper a stationary finite-state process is constructed that satisfies the ø-mixing condition but is not very weak Bernoulli with rate O(1/n). ø-mixing is implied by very weak Bernoulli with rate O(1/n), so this example shows very weak Bernoulli with rate O(1/n) is a strictly stronger condition.

Original language	English (US)
Pages (from-to)	117-133
Number of pages	17
Journal	Stochastic Processes and their Applications
Volume	50
Issue number	1
DOIs	https://doi.org/10.1016/0304-4149(94)90151-1
State	Published - Mar 1994

All Science Journal Classification (ASJC) codes

Statistics and Probability
Modeling and Simulation
Applied Mathematics

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10.1016/0304-4149(94)90151-1

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title = "Finite-state, stationary, {\o}-mixing processes which are not very weak Bernoulli with rate O(1/n)",

abstract = "In this paper a stationary finite-state process is constructed that satisfies the {\o}-mixing condition but is not very weak Bernoulli with rate O(1/n). {\o}-mixing is implied by very weak Bernoulli with rate O(1/n), so this example shows very weak Bernoulli with rate O(1/n) is a strictly stronger condition.",

author = "Burton, {Robert M.} and Manfred Denker and Doris Fiebig",

note = "Funding Information: Corres/?onrle~r to: Dr. Doris Fiebig, Institut fiir Angewandte Neuenheimer Feld 294, 6900 Heidelberg, Germany. * Supported in part by AFOSR #9l-0215, NSF #DMS-9103738.",

year = "1994",

month = mar,

doi = "10.1016/0304-4149(94)90151-1",

language = "English (US)",

volume = "50",

pages = "117--133",

journal = "Stochastic Processes and their Applications",

issn = "0304-4149",

publisher = "Elsevier B.V.",

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T1 - Finite-state, stationary, ø-mixing processes which are not very weak Bernoulli with rate O(1/n)

AU - Burton, Robert M.

AU - Denker, Manfred

AU - Fiebig, Doris

N1 - Funding Information: Corres/?onrle~r to: Dr. Doris Fiebig, Institut fiir Angewandte Neuenheimer Feld 294, 6900 Heidelberg, Germany. * Supported in part by AFOSR #9l-0215, NSF #DMS-9103738.

PY - 1994/3

Y1 - 1994/3

N2 - In this paper a stationary finite-state process is constructed that satisfies the ø-mixing condition but is not very weak Bernoulli with rate O(1/n). ø-mixing is implied by very weak Bernoulli with rate O(1/n), so this example shows very weak Bernoulli with rate O(1/n) is a strictly stronger condition.

AB - In this paper a stationary finite-state process is constructed that satisfies the ø-mixing condition but is not very weak Bernoulli with rate O(1/n). ø-mixing is implied by very weak Bernoulli with rate O(1/n), so this example shows very weak Bernoulli with rate O(1/n) is a strictly stronger condition.

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U2 - 10.1016/0304-4149(94)90151-1

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JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 1

ER -

Finite-state, stationary, ø-mixing processes which are not very weak Bernoulli with rate O(1/n)

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