Characterizations of generalized inverses associated with Markovian kernels
A systematic investigation of the various multicondition generalized inverses (g-inverses) of I-P, where P is the transition matrix of a finite, irreducible, discrete-time Markov chain is given. A completely efficient characterization of any g-inverse is based on the property of nonsingularity of the corresponding matrix with a minimal number of parameters. Partitioned forms for the g-inverses are given based on a full-rank factorization of the Markovian kernel, I-P. Special cases as the group inverses and the Moore-Penrose inverse are pointed out.
finite, irreducible, discrete- time Markov chain
scientific article; zbMATH DE number 4091660
scientific article