Abstract
Two classes of measure-valued processes (superprocesses and Fleming-Viot processes) are considered, and their historical structures are discussed. For representatives of both classes it is shown that although their fixed time distributions are closely related, their historical (genealogical) structures are mutually singular. This occurs due to the mutual singularity of random sequences describing the splitting times of the family trees of these processes.
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Dawson, D.A., Vinogradov, V. (1994). Mutual Singularity of Genealogical Structures of Fleming-Viot and Continuous Branching Processes. In: Freidlin, M.I. (eds) The Dynkin Festschrift. Progress in Probability, vol 34. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0279-0_2
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DOI: https://doi.org/10.1007/978-1-4612-0279-0_2
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