NDLI: Convex relative entropy decay in Markov chains

Content Provider	IEEE Xplore Digital Library
Author	Jog, V. Anantharam, V.
Copyright Year	2014
Description	Author affiliation: EECS, UC Berkeley, Berkeley, CA, USA (Jog, V.; Anantharam, V.)
Abstract	We look at irreducible continuous time Markov chains with a finite or countably infinite number of states, and a unique stationary distribution π. If the Markov chain has distribution $μ_{t}$ at time t, its relative entropy to stationarity is denoted by $h(μ_{t}\|π).$ This is a monotonically decreasing function of time, and decays to 0 at an exponential rate in most natural examples of Markov chains arising in applications. In this paper, we focus on the second derivative properties of $h(μ_{t}\|π).$ In particular we examine when relative entropy to stationarity exhibits convex decay, independent of the starting distribution. It has been shown that convexity of $h(μ_{t}\|π)$ in a Markov chain can lead to sharper bounds on the rate of relative entropy decay, and thus on the mixing time of the Markov chain. We study certain finite state Markov chains as well as countable state Markov chains arising from stable Jackson queueing networks.
Sponsorship	IEEE Inf. Theory Soc.
Starting Page	1
Ending Page	6
File Size	808640
Page Count	6
File Format	PDF
ISBN	9781479930012
DOI	10.1109/CISS.2014.6814159
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2014-03-19
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	convex decay Jackson network relative entropy Markov processes Routing Markov chains Entropy Vectors Equations Standards Convergence
Content Type	Text
Resource Type	Article

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3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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