Continuous dependence of a class of superprocesses on branching parameters and applications
This paper discusses the dependence of a finite-variance \((\xi,\Phi,k)\)-superprocess \(X\) on the branching mechanism \(\Phi(s,x,\lambda)\) and on the branching additive functional \(k(ds)\). In the general case where the one-particle motion \(\xi\) is a right process with càdlàg sample paths in a metrizable Luzin space \(E\), continuity of \(X\) with respect to \((\Phi,k)\) is obtained in the sense of convergence of the finite-dimensional marginals. Under the assumption that \(E\) is compact and \(\xi\) is a Hunt process, this result is sharpened to weak continuity of the law of \(X\) on Skorokhod space. In the latter context it is also shown that \(X\) itself possesses the Hunt property.
scientific article; zbMATH DE number 1355247