Expectations for Nonreversible Markov Chains

✍ Scribed by I.H. Dinwoodie

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 151 KB
• Volume: 220
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.1997.5850

✦ Synopsis

Bounds are given for an irreducible Markov chain on the probability that the time average of a functional on the state space exceeds its stationary expectation, without assuming reversibility. The bounds are in terms of the singular values of the discrete generator. ᮊ 1998 Academic Press

The probability of such deviations tends to zero by the weak law of large w x numbers, assuming that P is irreducible. The papers by Dinwoodie 8 and w x Gillman 12 were concerned with random walks on undirected graphs, or reversible chains, and the bounds involved only the spectrum of the 585