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On the \(2\)-orthogonal polynomials and the generalized birth and death processes. (English) Zbl 1129.60077

A generalized birth-death process is considered. In addition to the birth and death events defined in the usual birth-death process, simultaneous death of two particles is possible. The Chapman-Kolmogorov equations for the generalized birth-death process are derived and the infinitesimal generator is defined. Sufficient conditions are derived to provide an integral representation of the transition probabilities by establishing a bond between 2-orthogonal polynomials and these generalized birth-death processes.

MSC:

60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
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References:

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