Measure Concentration of Hidden Markov Processes
Abstract
We prove what appears to be the first concentration of measure result for hidden Markov processes. Our bound is stated in terms of the contraction coefficients of the underlying Markov process, and strictly generalizes the Markov process concentration results of Marton (1996) and Samson (2000). Somewhat surprisingly, the bound turns out to be the same as for ordinary Markov processes; this property, however, fails for general hidden/observed process pairs.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 August 2006
 arXiv:
 arXiv:math/0608064
 Bibcode:
 2006math......8064K
 Keywords:

 Mathematics  Probability;
 Mathematics  Functional Analysis;
 60G07;
 60J05
 EPrint:
 8 pages, 1 figure