Auto-Regressive Representations of a Stationary Markov Chain with Finite States.

2008-05-14T05:27:48Z

2008-05-14T05:27:48Z

1995-02-15

This paper deals with a nonlinear feedback system that transforms an independent stochastic sequence into a stationary Markov chain with finite states. As a nonlinear system, a stochastic difference equation is proposed with a nonlinear system function that is defined by the transition probability. Several types of auto-regressive (AR) representations for such a stochastic system are then introduced. First, an non-linear AR equation is derived by expanding the system function　into a power series. The Markov chain is then represented by a K-dimensional vector which enjoys a linear discrete-valued AR equation, where　K is the number of states. Third, the Markov chain is represented by a unit vector sequence, which satisfies another linear discrete-valued AR equation. Further, the Markov chain is regarded as a (K-1)-dimensional vector sequence, which satisfies a linear AR equation with a constant coefficient matrix and white noise excitation. Relationships between these representations are discussed and formulas for spectrum matrix, correlation matrix and joint probability are obtained.

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京都工芸繊維大学　工芸学部研究報告　第４３巻　理工・欧文(1994) pp.27-39

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