Abstract
By G we shall denote the class of sets of birth-death parameters {λn, μn: n = 0, 1....} with μ0 = 0, and by G* the class of sets of birth-death parameters {λ *n , μ *n : n = 0, 1,...} with μ *0 > 0. The mapping f: G → G* defined by
where
clearly establishes a 1 – 1 correspondence between the elements of G and G*. Now let {λn,μn} ∈ G and {λ *n , μ *n } = f({λn,μn})∈ G* be two related sets of birth-death parameters and {πn}, respectively {π *n }, the associated potential coefficients. The following identities are easily verified in view of (1.3.3) and (3.1.2).
and(3.1.4)
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© 1981 Springer-Verlag New York Inc.
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van Doorn, E.A. (1981). Dual Birth-Death Processes. In: Stochastic Monotonicity and Queueing Applications of Birth-Death Processes. Lecture Notes in Statistics, vol 4. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5883-4_3
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DOI: https://doi.org/10.1007/978-1-4612-5883-4_3
Publisher Name: Springer, New York, NY
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