Abstract
Let \( \Phi = \left\{ {{\Phi _n}} \right\} \)be a Markov chain on a half-line [0, ∞) that is stochastically ordered in its initial state. We find conditions under which there are explicit bounds on the rate of convergence of the chain to a stationary limit π: specifically, for suitable rate functions r which may be geometric or subgeometric and “moments” f ≥ 1, we find conditions under which
for all n and all x. We find bounds on r ( n ) and M(x) both in terms of geometric and subgeometric “drift functions”, and in terms of behaviour of the hitting times on {0} and on compact sets [0 c ] for c > 0. The results are illustrated for random walks and for a multiplicative time series model.
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Work supported in part by NSF Grants DMS-9205687 and DMS-9504561
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Scott, D.J., Tweedie, R.L. (1996). Explicit Rates of Convergence of Stochastically Ordered Markov Chains*. In: Heyde, C.C., Prohorov, Y.V., Pyke, R., Rachev, S.T. (eds) Athens Conference on Applied Probability and Time Series Analysis. Lecture Notes in Statistics, vol 114. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0749-8_12
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