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,
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).
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Dawson, D.A., Fleischmann, K., Roelly, S. (1991). Absolute Continuity of the Measure States in a Branching Model with Catalysts. In: Çinlar, E., Fitzsimmons, P.J., Williams, R.J. (eds) Seminar on Stochastic Processes, 1990. Progress in Probability, vol 24. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4684-0562-0_5
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DOI: https://doi.org/10.1007/978-1-4684-0562-0_5
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