On the Ergodicity of Gaussian Periodically Correlated Stochastic Processes
Summary :
A necessary and sufficient condition of the ergodicity for a class of Gaussian periodically correlated stochastic processes is given in this paper. Periodically correlated processes are also called cyclostationary processes in wide sense, and these are mainly studied as models of signal processes in the communication theory and as models of time series of practical data of stochastic phenomena in some periodical environment. On the line of Boyles and Gardner's study(10) on cycloergodicity of certain class of nonstationary processes of discrete time parameter, we reformulate such ergodicity of cyclostationary processes in strict sense in continuous time parameter case, and prove a ergodic theorem. Futhermore, we apply it to Gaussian periodically correlated process, and discuss almost sure limiting behavior of a sample periodogram of the process.
- Publication
- IEICE TRANSACTIONS on transactions Vol.E73-E No.10 pp.1729-1737
- Publication Date
- 1990/10/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- PAPER
- Category
- Foundations of Signal Theory and Communication Theory
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Ikuji HONDA, "On the Ergodicity of Gaussian Periodically Correlated Stochastic Processes" in IEICE TRANSACTIONS on transactions,
vol. E73-E, no. 10, pp. 1729-1737, October 1990, doi: .
Abstract: A necessary and sufficient condition of the ergodicity for a class of Gaussian periodically correlated stochastic processes is given in this paper. Periodically correlated processes are also called cyclostationary processes in wide sense, and these are mainly studied as models of signal processes in the communication theory and as models of time series of practical data of stochastic phenomena in some periodical environment. On the line of Boyles and Gardner's study(10) on cycloergodicity of certain class of nonstationary processes of discrete time parameter, we reformulate such ergodicity of cyclostationary processes in strict sense in continuous time parameter case, and prove a ergodic theorem. Futhermore, we apply it to Gaussian periodically correlated process, and discuss almost sure limiting behavior of a sample periodogram of the process.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e73-e_10_1729/_p
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@ARTICLE{e73-e_10_1729,
author={Ikuji HONDA, },
journal={IEICE TRANSACTIONS on transactions},
title={On the Ergodicity of Gaussian Periodically Correlated Stochastic Processes},
year={1990},
volume={E73-E},
number={10},
pages={1729-1737},
abstract={A necessary and sufficient condition of the ergodicity for a class of Gaussian periodically correlated stochastic processes is given in this paper. Periodically correlated processes are also called cyclostationary processes in wide sense, and these are mainly studied as models of signal processes in the communication theory and as models of time series of practical data of stochastic phenomena in some periodical environment. On the line of Boyles and Gardner's study(10) on cycloergodicity of certain class of nonstationary processes of discrete time parameter, we reformulate such ergodicity of cyclostationary processes in strict sense in continuous time parameter case, and prove a ergodic theorem. Futhermore, we apply it to Gaussian periodically correlated process, and discuss almost sure limiting behavior of a sample periodogram of the process.},
keywords={},
doi={},
ISSN={},
month={October},}
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TY - JOUR
TI - On the Ergodicity of Gaussian Periodically Correlated Stochastic Processes
T2 - IEICE TRANSACTIONS on transactions
SP - 1729
EP - 1737
AU - Ikuji HONDA
PY - 1990
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E73-E
IS - 10
JA - IEICE TRANSACTIONS on transactions
Y1 - October 1990
AB - A necessary and sufficient condition of the ergodicity for a class of Gaussian periodically correlated stochastic processes is given in this paper. Periodically correlated processes are also called cyclostationary processes in wide sense, and these are mainly studied as models of signal processes in the communication theory and as models of time series of practical data of stochastic phenomena in some periodical environment. On the line of Boyles and Gardner's study(10) on cycloergodicity of certain class of nonstationary processes of discrete time parameter, we reformulate such ergodicity of cyclostationary processes in strict sense in continuous time parameter case, and prove a ergodic theorem. Futhermore, we apply it to Gaussian periodically correlated process, and discuss almost sure limiting behavior of a sample periodogram of the process.
ER -
English
