## Abstract

We consider a discrete-time Markov chain (Xt,Yt), t=0,1,2,..., where the X-component forms a Markov chain itself. Assume that (Xt) is Harris-ergodic and consider an auxiliary Markov chain Y^t whose transition probabilities are the averages of transition probabilities of the Y-component of the (X,Y)-chain, where the averaging is weighted by the stationary distribution of the X-component.

We first provide natural conditions in terms of test functions ensuring that the Y^-chain is positive recurrent and then prove that these conditions are also sufficient for positive recurrence of the original chain (Xt,Yt). The we prove a "multi-dimensional" extension of the result obtained. In the second part of the paper, we apply our results to two versions of a multi-access wireless model governed by two randomised protocols.

We first provide natural conditions in terms of test functions ensuring that the Y^-chain is positive recurrent and then prove that these conditions are also sufficient for positive recurrence of the original chain (Xt,Yt). The we prove a "multi-dimensional" extension of the result obtained. In the second part of the paper, we apply our results to two versions of a multi-access wireless model governed by two randomised protocols.

Original language | English |
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Pages (from-to) | 208-231 |

Number of pages | 24 |

Journal | Stochastic Systems |

Volume | 2 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2012 |