Continuous dependence of a class of superprocesses on branching parameters and applications

• 成果类型: Article
• 署名作者: Dawson, DA; Fleischmann, K; Leduc, G
• 署名单位: Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Quebec; University of Quebec Montreal
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1998
• 页码: 562-601
• 关键词: regularity

摘要

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 Phi 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) = rho(s)(xi(s))ds [that is, a branching functional k generated by a classical branching rate rho(s)(gamma)] 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.