Characteristic of exit moments and models of enlargement of states for finite Markov chains in terms of global memory functionals
Anisimov, V. V.
Klygunova, Y. Y.
Cybernetics and Systems Analysis
405 - 414
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A notion of local- and global-memory functions for discrete-type distributions is introduced by analogy with the notion of the memory for continuous-type distributions introduced in Muth's papers. In the class of PH-distributions (i.e., of distributions of the time of Markov chain exit from a subset of states) the necessary and sufficient conditions are obtained for the case where the exit time has an exponential (continuous-time) or a geometric (discrete time) distribution. A new notion of a global memory functional for decomposition of the state space of a finite Markov chain is introduced. Its properties as a measure of quality of decomposition and enlargement of a state space are studied. The asymptotic optimality is proved. © 2000 Kluwer Academic/Plenum Publishers.