Abstract
In this chapter we prove some basic regularities of Dawson–Watanabe superprocesses. We shall develop the theory in the Borel right setting, which is particularly suitable for the applications of various transformations. We shall see that if the underlying spatial motion ξ is a Borel right process, the (ξ,φ)-superprocess is a Borel right process with quasi-left continuous natural filtration; and if ξ is a Hunt process, so is the superprocess. We also give a characterization of the so-called occupation times of the superprocess.
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© 2011 Springer-Verlag Berlin Heidelberg
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Li, Z. (2011). Basic Regularities of Superprocesses. In: Measure-Valued Branching Markov Processes. Probability and Its Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15004-3_5
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DOI: https://doi.org/10.1007/978-3-642-15004-3_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15003-6
Online ISBN: 978-3-642-15004-3
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