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Construction and regularity of measure-valued markov branching processes

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Abstract

A construction is given for a general class of measure-valued Markov branching processes. The underlying spatial motion process is an arbitrary Borel right Markov process, and state-dependent offspring laws are allowed. It is shown that such processes are Hunt processes in the Ray weak* topology, and have continuous paths if and only if the total mass process is continuous. The entrance spaces of such processes are described explicitly.

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Authors and Affiliations

  1. Department of Mathematics, C-012, University of California, 92093, San Diego, La Jolla, CA, USA

    P. J. Fitzsimmons

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  1. P. J. Fitzsimmons
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Research supported in part by NSF Grant DMS 87-21237.

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Fitzsimmons, P.J. Construction and regularity of measure-valued markov branching processes. Israel J. Math. 64, 337–361 (1988). https://doi.org/10.1007/BF02882426

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  • DOI: https://doi.org/10.1007/BF02882426

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