Absolute continuity of catalytic measure-valued branching processes.
A catalytic measure-valued branching process in \(\mathbb R^d\) with a Feller motion process \(\xi \) is studied, where the branching rate is given by a continuous additive functional of \(\xi \) and where the branching law may vary in space and time. A sufficient condition for absolute continuity of the values of the process with respect to Lebesgue measure is given. The condition is sharp for the classical cases. Conversely, a sufficient condition for singularity of the states is also provided.
scientific article; zbMATH DE number 2098350