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Monotone Markov chains

  • Masaaki Kijima

Abstract

In this chapter, we consider the monotonicity properties of discrete-time Markov chains where each monotonicity is characterized in terms of transition matrices. A Markov chain {X n }is said to be increasing (decreasing, respectively) if X n+1X n (X n X n+1) for all n = 0,1, ..., where ≻ denotes an ordering relation in some stochastic sense, and in either case we call {X n }internally monotone, or monotone for short. An external monotonicity is such that, for two Markov chains {X n }and {Y n , we have X n Y n for all n. Monotonicity properties are important both theoretically and practically because they lead to a variety of structural insights. In particular, they are a basic tool for deriving many useful inequalities in Markov chains for stochastic modeling.

Keywords

Markov Chain Hazard Rate Probability Vector Discrete Random Variable Service Time Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© M. Kijima 1997

Authors and Affiliations

  • Masaaki Kijima
    • 1
  1. 1.Graduate School of Systems ManagementUniversity of TsukubaTokyoJapan

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