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Convergence Property of Standard Transition Functions

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Markov Processes and Controlled Markov Chains

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Abstract

A standard transition function P = (P ij (t)) is called ergodic (positive recurrent) if there exists a probability measure π = (π i ; i ∈ E) such that

$$ \mathop{{\lim }}\limits_{{t \to \infty }} {{p}_{i}}_{j}(t) = {{\pi }_{j}} > 0,\forall i \in E $$
(0.1)

The aim of this paper is to discuss the convergence problem in (0.1). We shall study four special types of convergence: the so-called strong ergodicity, uniform polynomial convergence, L 2-exponential ergodicity and exponential ergodicity. Our main interest is always to characterize these properties in terms of the q-matrix.

Supported by the National Natural Science Foundation of China (19871006)

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Author information

Authors and Affiliations

  1. Research Department, Changsha Railway University, Changsha, Hunan, 410075, China

    Hanjun Zhang, Qixiang Mei, Xiang Lin & Zhenting Hou

Authors
  1. Hanjun Zhang
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  2. Qixiang Mei
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  3. Xiang Lin
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  4. Zhenting Hou
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Editor information

Editors and Affiliations

  1. Research Department, Changsha Railway University, Changsha, China

    Zhenting Hou

  2. School of Mathematics, University of South Australia, Mawson Lakes, SA, Australia

    Jerzy A. Filar

  3. School of Computing and Mathematical Sciences, University of Greenwich, London, UK

    Anyue Chen

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© 2002 Kluwer Academic Publishers

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Zhang, H., Mei, Q., Lin, X., Hou, Z. (2002). Convergence Property of Standard Transition Functions. In: Hou, Z., Filar, J.A., Chen, A. (eds) Markov Processes and Controlled Markov Chains. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0265-0_4

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  • DOI: https://doi.org/10.1007/978-1-4613-0265-0_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7968-3

  • Online ISBN: 978-1-4613-0265-0

  • eBook Packages: Springer Book Archive

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