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Necessary and sufficient conditions for a matrix to be causative in a nonstationary Markov chain

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  • Hennessey, John
  • Bye, Barry V.

Abstract

Given a sequence of transition matrices for a nonstationary Markov chain, a matrix whose product on the right of a transition matrix yields the next transition matrix is called a causative matrix. A causative matrix is strongly causative if successive products continue to yield stochastic matrices. This paper presents necessary and sufficient conditions for a matrix to be causative and strongly causative with respect to an invertible transition matrix, by considering the causative matrix as a linear transformation on the rows of the transition matrix.

Suggested Citation

  • Hennessey, John & Bye, Barry V., 1979. "Necessary and sufficient conditions for a matrix to be causative in a nonstationary Markov chain," Stochastic Processes and their Applications, Elsevier, vol. 8(3), pages 305-314, May.
    • Handle: RePEc:eee:spapps:v:8:y:1979:i:3:p:305-314
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