The complete characterization of a general class of superprocesses (Q1566936)

It is known that under mild conditions the log-Laplace functional of every measure-valued process is a solution of an evolution equation determined by three parameters \(\xi, Q \) and \(l\). The author establishes the converse of the above mentioned result. Namely, he considers a general class \({\mathcal H}\) of branching measure-valued processes \(X\) and shows that every process \(X\in {\mathcal H}\) is a \((\xi , \Phi, K)\)-superprocess with \(\xi , \Phi, K\) satisfying some mild conditions and, conversly, for each of the triples satisfying these conditions there exists a version \(X\) of \((\xi , \Phi, K)\)-superprocesses which belongs to \({\mathcal H}\). This gives the full characterization of \({\mathcal H}\) in terms of the imposed conditions.