CHARACTERISTIC OF EXIT MOMENTS AND MODELS OF ENLARGEMENT OF STATES FOR FINITE MARKOV CHAINS IN TERMS OF GLOBAL MEMORY FUNCTIONS

摘要

A notion of local- and global-memory functional 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.