FUNCTIONS OF PROCESSES WITH MARKOVIAN STATES.
MICHIGAN STATE UNIV EAST LANSING DEPT OF STATISTICS
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Given a process Yn, let epsilon be a state of finite rank. An example is given in which Yn fXn, Xn is countable state, stationary, Markov, Yn is stationary with one state each of ranks 1 and 3, yet it is impossible to take Xn to be finite state Markov. In general it is proved that Yn fXn where epsilon fepsilon i i 1,2,..., delta fdelta for delta not equal to epsilon and the epsilon i are Markovian states. If epsilon has rank 2 it is proved that two states suffice and that the rank of delta not equal to epsilon in Xn is the same as in Yn. Finally, it is proved that if epsilon has rank 2 and Yn is stationary, Xn is stationary. Author
- Statistics and Probability