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Markov random processes are neither bandlimited nor recoverable from samples or after quantization

Marco, Daniel (2009) Markov random processes are neither bandlimited nor recoverable from samples or after quantization. IEEE Transactions on Information Theory, 55 (2). pp. 900-905. ISSN 0018-9448. https://resolver.caltech.edu/CaltechAUTHORS:20090415-144137698

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Abstract

This paper considers basic questions regarding Markov random processes. It shows that continuous-time, continuous-valued, wide-sense stationary, Markov processes that have absolutely continuous second-order distribution and finite second moment are not bandlimited. It also shows that continuous-time, stationary, Markov processes that are continuous-valued or discrete-valued and satisfy additional mild conditions cannot be recovered from uniform sampling. Further it shows that continuous-time, continuous-valued, stationary, Markov processes that have absolutely continuous second-order distributions and are continuous almost surely, cannot be recovered without error after quantization. Finally, it provides necessary and sufficient conditions for stationary, discrete-time, Markov processes to have zero entropy rate, and relates this to information singularity.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/TIT.2008.2009797DOIUNSPECIFIED
http://ieeexplore.ieee.org/search/wrapper.jsp?arnumber=4777624PublisherUNSPECIFIED
Additional Information:© 2009 IEEE. Manuscript received January 16, 2007; revised June 30, 2008. Current version published February 04, 2009. This work was supported by the Center for the Mathematics of Information at California Institute of Technology. The material in this paper was presented in part at the IEEE International Symposium on Information Theory, Nice, France, June 2007. The author is grateful to David L. Neuhoff for his careful reading of the original manuscript and his valuable comments and suggestions. He also thanks Jose A. Costa for helpful discussions, and he thanks the anonymous reviewer for his/her very useful remarks.
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Funding AgencyGrant Number
Center for the Mathematics of Information at California Institute of TechnologyUNSPECIFIED
Subject Keywords:bandlimited; information-singular; Markov; recoverability after quantization; recoverability from samples
Issue or Number:2
Record Number:CaltechAUTHORS:20090415-144137698
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20090415-144137698
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:13989
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:16 Apr 2009 21:25
Last Modified:03 Oct 2019 00:46

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