CONTINUOUS DEPENDENCE OF A CLASS OF SUPERPROCESSES ON BRANCHING PARAMETERS AND APPLICATIONS

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.