On the Internal Structure of Finite-State Stochastic Processes
The “Identifiabi1ity problem for functions of finite Markov chains”, which we might now rather call “the finite-state stochastic realization problem”, was stated by BLACKWELL and KOOPMANS  in 1957. Even if there exists now a rather abundant literature on this subject, yet, it can safely be asserted that very little progress has been made. This is especially true as for an algorithmic solution is concerned. This actually shows that the problem is a very hard one (though an important one).
KeywordsStochastic System Stochastic Matrix Polyhedral Convex Hankel Matrix Stationary Stochastic Process
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- Carlyle, J.W. “Stochastic finite-state system theory”. In System Theory (L.A. Zadeh, and E. Polak eds.), chapter 10. McGraw-Hill, New York (1969).Google Scholar
- Dharmadhikari, S.W., “Some nonregular functions of finite Markov chains”. Rep. No. RM.-202, SD-2 (1967) Michigan State University.Google Scholar
- Paz, A., Introduction to probabilistic automata. Ac. Press, New York (1971).Google Scholar
- Fliess, M. “Series rationelles positives et processus stochastiques” Ann. Inst. Henri Poincaré, XI, 1, (1975) 1–21.Google Scholar
- Kalman, R.E., Falb, P.L., Arbib, M., Topics in mathematical system theory. Mc Graw-Hill, New York (1969).Google Scholar