Open Access
April 1998 Continuous dependence of a class of superprocesses on branching parameters and applications
Donald A. Dawson, Klaus Fleischmann, Guillaume Leduc
Ann. Probab. 26(2): 562-601 (April 1998). DOI: 10.1214/aop/1022855644


A general class of finite variance critical $(\xi, \Phi, k)$-superprocesses $X$ in a Luzin space $E$ with cadlag right Markov motion process $\xi$, regular local branching mechanism and branching functional $k$ of bounded characteristic are shown to continuously depend on $(\Phi, k)$. As an application we show that the processes with a classical branching functional $k(ds) = \varrho_s (\xi_s) ds [that is, a branching functional $k$ generated by a classical branching rate $\varrho_s (y)] are dense in the above class of $(\xi, \Phi, k)$-superprocesses $X$. Moreover, we show that, if the phase space $E$ is a compact metric space and $\xi$ is a Feller process, then always a Hunt version of the $(\xi, \Phi, k)$-superprocess $X$ exists. Moreover, under this assumption, we even get continuity in $(\Phi, k)$ in terms of weak convergence of laws on Skorohod path spaces.


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Donald A. Dawson. Klaus Fleischmann. Guillaume Leduc. "Continuous dependence of a class of superprocesses on branching parameters and applications." Ann. Probab. 26 (2) 562 - 601, April 1998.


Published: April 1998
First available in Project Euclid: 31 May 2002

zbMATH: 0938.60078
MathSciNet: MR1626507
Digital Object Identifier: 10.1214/aop/1022855644

Primary: 60J80
Secondary: 60G57 , 60J40

Keywords: branching functional of bounded characteristic , cadlag right process , catalytic branching rate , continuity theorem , Feller process , Hunt process , log-Laplace functional , measure-valued branching , regular local branching mechanism , Skorohod path space , Superprocess , weak convergence on path spaces

Rights: Copyright © 1998 Institute of Mathematical Statistics

Vol.26 • No. 2 • April 1998
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