UPPER BOUNDS OF A MEASURE OF DEPENDENCE AND THE RELAXATION TIME FOR FINITE STATE MARKOV CHAINS

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概要

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• In this paper, we consider a measure of dependence between X_t and X_0 where X_t is an irreducible Markov chain on a finite state space. Namely, we define d_t(X) = sup_<f,g>Cor [f(<X^^^>_0),g(<X^^^>_t)]. Here <X^^^>_t is the stationary process associated with X_t and the supreme is taken over all real functions. An upper bound of d_t(X), which is easy to calculate numerically, is derived. By showing a simple relation between d_t(X) and the relaxation time T_<REL>(X) of X_<t'> we also provide an upper bound of T_<REL>(X). The bounds are shown to be tight when the Markov chain is reversible in time.

• 社団法人日本オペレーションズ・リサーチ学会の論文

著者

• Kijima M

  Department Of Information Sciences Tokyo Institute Of Technology

• Kijima Masaaki

  Department Of Information Sciences Tokyo Institute Of Technology

関連論文

• ON THE RELAXATION TIME FOR SINGLE SERVER QUEUES
• UPPER BOUNDS OF A MEASURE OF DEPENDENCE AND THE RELAXATION TIME FOR FINITE STATE MARKOV CHAINS

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