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. doi:10.1109/TIT.2008.2009797. 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 | |||||||||
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| 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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| Subject Keywords: | bandlimited; information-singular; Markov; recoverability after quantization; recoverability from samples | |||||||||
| Issue or Number: | 2 | |||||||||
| DOI: | 10.1109/TIT.2008.2009797 | |||||||||
| 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: | 08 Nov 2021 22:42 |
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