caa a22 4500 386350361 CHVBK 20180307111827.0 cr unu---uuuuu 161130e198901 xx s 000 0 eng 10.1017/S026996480000098X doi S026996480000098X pii (NATIONALLICENCE)cambridge-10.1017/S026996480000098X Spectral Theory for Skip-Free Markov Chains [Elektronische Daten] The distribution of upward first passage times in skip-free Markov chains can be expressed solely in terms of the eigenvalues in the spectral representation, without performing a separate calculation to determine the eigenvectors. We provide insight into this result and skip-free Markov chains more generally by showing that part of the spectral theory developed for birth-and-death processes extends to skip-free chains. We show that the eigenvalues and eigenvectors of skip-free chains can be characterized in terms of recursively defined polynomials. Moreover, the Laplace transform of the upward first passage time from 0 to n is the reciprocal of the nth polynomial. This simple relationship holds because the Laplace transforms of the first passage times satisfy the same recursion as the polynomials except for a normalization. Copyright © Cambridge University Press 1989 Abate Joseph AT&T Bell Laboratories Whippany, New Jersey 07981 Whitt Ward AT&T Bell Laboratories Murray Hill, New Jersey 07974 Probability in the Engineering and Informational Sciences Cambridge University Press 3/1(1989-01), 77-88 0269-9648 3:1<77 1989 3 PES https://doi.org/10.1017/S026996480000098X text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S026996480000098X text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Abate Joseph AT&T Bell Laboratories Whippany, New Jersey 07981 NATIONALLICENCE 700 1- Whitt Ward AT&T Bell Laboratories Murray Hill, New Jersey 07974 NATIONALLICENCE 773 0- Probability in the Engineering and Informational Sciences Cambridge University Press 3/1(1989-01), 77-88 0269-9648 3:1<77 1989 3 PES CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge