An Orthogonal-Polynomial Approach to First-Hitting Times of Birth–Death Processes
نویسنده
چکیده
In a recent paper in this journal, Gong, Mao and Zhang, using the theory of Dirichlet forms, extendedKarlin andMcGregor’s classical results on first-hitting times of a birth–death process on the nonnegative integers by establishing a representation for the Laplace transform E[esTi j ] of the first-hitting time Ti j for any pair of states i and j , as well as asymptotics for E[esTi j ] when either i or j tends to infinity. It will be shown here that these results may also be obtained by employing tools from the orthogonal-polynomial toolbox used byKarlin andMcGregor, in particular associated polynomials and Markov’s theorem.
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