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

John Hennessey and Barry V. Bye

Stochastic Processes and their Applications, 1979, vol. 8, issue 3, 305-314

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.

Keywords: Linear; transformation; characteristic; values; characteristic; vectors; characteristic; subspaces; systems; of; linear; inequalities; causative; matrix; primary; decomposition; theorem; constant; causative; matrix; chain (search for similar items in EconPapers)
Date: 1979
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