Abstract
In this paper the elements of a semi-Markov matrix A may have support anywhere on the real line, and A(+ co) may be a sub-Markov matrix. The sub-characteristic matrix a of A is the matrix of Fourier-Stieltjes transforms corresponding to A. If A(+ co) = a(O) is a Markov matrix, A is called a matrix distribution funotion and at a characteristic matrix. Infinite divisibility and stability of semi-Markov and sub-characteristic matrices is defined as for distribution functions and characteristic functions.
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