General linear-fractional branching processes with discrete time |
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Authors: | Alexey Lindo |
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Institution: | School of Mathematics and Statistics, University of Glasgow, Glasgow, UK. |
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Abstract: | We study a linear-fractional Bienaymé–Galton–Watson process with a general type space. The corresponding tree contour process is described by an alternating random walk with the downward jumps having a geometric distribution. This leads to the linear-fractional distribution formula for an arbitrary observation time, which allows us to establish transparent limit theorems for the subcritical, critical and supercritical cases. Our results extend recent findings for the linear-fractional branching processes with countably many types. |
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Keywords: | General linear-fractional distribution general Markov chains and irreducible kernels Bienaymé–Galton–Watson process with a general type space Crump–Mode–Jagers process |
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