A class of Markov chains with no spectral gap Public Deposited

http://ir.library.oregonstate.edu/concern/articles/dv13zw057

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  • In this paper we extend the results of the research started by the first author in which Karlin-McGregor diagonalization of certain reversible Markov chains over countably infinite general state spaces by orthogonal polynomials was used to estimate the rate of convergence to a stationary distribution. We use a method of Koornwinder to generate a large and interesting family of random walks which exhibits a lack of spectral gap, and a polynomial rate of convergence to the stationary distribution. For the Chebyshev type subfamily of Markov chains, we use asymptotic techniques to obtain an upper bound of order O (log t/√t) and a lower bound of order O (1/√t) on the distance to the stationary distribution regardless of the initial state. Due to the lack of a spectral gap, these results lie outside the scope of geometric ergodicity theory.
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  • Kovchegov, Y., & Michalowski, N. (2013). A class of Markov chains with no spectral gap. Proceedings of the American Mathematical Society, 141(12), 4317-4326. doi:10.1090/S0002-9939-2013-11697-7
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  • description.provenance : Submitted by Deanne Bruner (deanne.bruner@oregonstate.edu) on 2014-02-28T18:46:20ZNo. of bitstreams: 1KovchegovYevgeniyMathematicsClassMarkovChains.pdf: 196963 bytes, checksum: 0bd078825248cb764fb0edefd04324a6 (MD5)
  • description.provenance : Approved for entry into archive by Deanne Bruner(deanne.bruner@oregonstate.edu) on 2014-02-28T18:47:27Z (GMT) No. of bitstreams: 1KovchegovYevgeniyMathematicsClassMarkovChains.pdf: 196963 bytes, checksum: 0bd078825248cb764fb0edefd04324a6 (MD5)
  • description.provenance : Made available in DSpace on 2014-02-28T18:47:27Z (GMT). No. of bitstreams: 1KovchegovYevgeniyMathematicsClassMarkovChains.pdf: 196963 bytes, checksum: 0bd078825248cb764fb0edefd04324a6 (MD5) Previous issue date: 2013-12

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