Abstract
Spatially homogeneous measure-valued branching Markov processes X on the real line ℝ with certain motion processes and branching mechanisms with finite variances have absolutely continuous states with respect to Lebesgue measure, that is, roughly speaking,$$X(t,dy) = \eta (t,y)dy$$ for some random density function η(t)=η(t,·). Results of this type are established in Dawson and Hochberg (1979), Roelly-Coppoletta (1986), Wulfsohn (1986), Konno and Shiga (1988), and Tribe (1989).KeywordsContinuous StateRandom MeasureRandom MediumAbsolute ContinuityBasic LemmaThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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