Continuous dependence of a class of superprocesses on branching parameters and applications
- Dawson, Donald A.
- Fleischmann, Klaus
- Leduc, Guillaume
2010 Mathematics Subject Classification
- 60J80 60J40 60G57
- branching functional of bounded characteristic, measurevalued branching, regular local branching mechanism, càdlàg right process, Hunt process, Feller process, weak convergence on path spaces, continuity theorem, log-Laplace functional, Skorohod path space, catalytic branching rate
A general class of finite variance critical (ξ,ɸ,k)-superprocesses X in a Luzin space E with càdlàg right motion process ξ, regular local branching mechanism ɸ, and branching functional k of bounded characteristic are shown to continuously depend on (ɸ,k). As an application we show that the processes with a classical branching functional k(ds) = ϱs(ξs)ds (that is a branching functional k generated by a classical branching rate ϱs(y)) are dense in the above class of (ξ,ɸ,k)-superprocesses X. Moreover, we show that, if the phase space E is a compact metric space and ξ is a Feller process, then always a Hunt version of the (ξ,ɸ,k)-superprocess X exists. Moreover, under this assumption, we even get continuity in (ɸ,k) in terms of weak convergence of laws on Skorohod path spaces.
- Ann. Probab., 26 (1998), pp. 262-301