Auto-Regressive Representations of a Stationary Markov Chain with Finite States.
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type:Article
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.
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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- CRID
- 1050001337582497024
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- NII論文ID
- 120000794784
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- http://hdl.handle.net/10212/1729
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- en
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- journal article
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