In:
Advances in Applied Probability, Cambridge University Press (CUP), Vol. 24, No. 02 ( 1992-06), p. 322-342
Abstract:
We consider a family of irreducible, ergodic and aperiodic Markov chains X (ε) = {X (ε) n , n ≧0} depending on a parameter ε & gt; 0, so that the local drifts have a critical behaviour (in terms of Pakes' lemma). The purpose is to analyse the steady-state distributions of these chains (in the sense of weak convergence), when ε↓ 0. Under assumptions involving at most the existence of moments of order 2 + γ for the jumps, we show that, whenever X (0) is not ergodic, it is possible to characterize accurately these limit distributions. Connections with the gamma and uniform distributions are revealed. An application to the well-known ALOHA network is given.
Type of Medium:
Online Resource
ISSN:
0001-8678
,
1475-6064
DOI:
10.1017/S0001867800047558
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
1992
detail.hit.zdb_id:
1474602-5
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