Summary
This paper is concerned with Markov processes with continuous creation where the phase space is a general separable compact metric space. The transition probabilities for such a process determine a semigroup of operators acting on a function space over the collection of bounded Borel measures on the phase space. Such a semigroup is characterized by a particular convolution condition and is called a continuous state branching semigroup. A connection is established between continuous state branching semigroups and certain semigroups of nonlinear operators and then this connection is exploited to establish an existence theorem for the former.
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Research associated with a project in probability at Princeton University supported by the Office of Army Research.
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Silverstein, M.L. Continuous state branching semigroups. Z. Wahrscheinlichkeitstheorie verw Gebiete 14, 96–112 (1969). https://doi.org/10.1007/BF00537516
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DOI: https://doi.org/10.1007/BF00537516