Convergence parameter associated with a Markov chain and a family of functions |
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Authors: | M G Shur |
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Institution: | 1. Moscow State Institute of Electronics and Mathematics, Moscow, Russia
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Abstract: | The proposed definition of convergence parameter R(W) corresponding to a Markov chain X with a measurable state space (E,?) and any nonempty setW of bounded below measurable functions f: E → ? is wider than the well-known definition of convergence parameter R in the sense of Tweedie or Nummelin. Very often, R(W) < ∞, and there exists a set playing the role of the absorbing set inNummelin’s definition ofR. Special attention is paid to the case in whichE is locally compact, X is a Feller chain on E, and W coincides with the family ? 0 + of all compactly supported continuous functions f ≥ 0 (f ? 0). In particular, certain conditions for R(? 0 + )?1 to coincide with the norm of an appropriate modification of the chain transition operator are found. |
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