Factorization of Markov chains (Q1827454)

Let \(A\) be a (sub)stochastic \(d\times d\) matrix, with \(d=\infty\) possible. Existence of a factorization \(I-A=(I-B)(I-C)\) is proved for matrices \(B\) and \(C\) which are in particular triangular. The purpose is to solve in two steps equations \((I-A)x=g\) by recurrence. The author's paper [Sb. Math. 189, No. 12, 1795--1808 (1998); translation from Mat. Sb. 189, No.~12, 59--72 (1998; Zbl 0932.45005)] considered the case \(d<\infty\). This paper is particularly devoted to the case \(d=\infty\), with controls of the infinite sequences determined by recurrence.