Da. Dawson et al., CONTINUOUS DEPENDENCE OF A CLASS OF SUPERPROCESSES ON BRANCHING PARAMETERS AND APPLICATIONS, Annals of probability, 26(2), 1998, pp. 562-601
A general class of finite variance critical (xi, Phi, k)-superprocesse
s X in a Luzin space E with cadlag right Markov motion process xi, reg
ular local branching mechanism Phi and branching functional k of bound
ed characteristic are shown to continuously depend on (Phi, k). As an
application we show that the processes with a classical branching func
tional k(ds) = rho(s)(xi(s))ds [that is, a branching functional k gene
rated by a classical branching rate rho(s)(gamma)] are dense in the ab
ove 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 proces
s, then always a Hunt version of the (xi, Phi, k)-superprocess X exist
s. Moreover, under this assumption, we even get continuity in (Phi, k)
in terms of weak convergence of laws on Skorohod path spaces.