Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Locally contracting iterated functions and stability of Markov chains.
AU - Jarner, S. F.
AU - Tweedie, R. L.
PY - 2001
Y1 - 2001
N2 - We consider Markov chains in the context of iterated random functions and show the existence and uniqueness of an invariant distribution under a local contraction condition combined with a drift condition, extending results of Diaconis and Freedman. From these we deduce various other topological stability properties of the chains. Our conditions are typically satisfied by, for example, queueing and storage models where the global Lipschitz condition used by Diaconis and Freedman normally fails.
AB - We consider Markov chains in the context of iterated random functions and show the existence and uniqueness of an invariant distribution under a local contraction condition combined with a drift condition, extending results of Diaconis and Freedman. From these we deduce various other topological stability properties of the chains. Our conditions are typically satisfied by, for example, queueing and storage models where the global Lipschitz condition used by Diaconis and Freedman normally fails.
KW - Markov chains
KW - iterated functions
KW - geometric convergence
KW - stochastic monotonicity
KW - rates of convergence
U2 - 10.1239/jap/996986758
DO - 10.1239/jap/996986758
M3 - Journal article
VL - 38
SP - 494
EP - 507
JO - Journal of Applied Probability
JF - Journal of Applied Probability
IS - 2
ER -