Super-Brownian motions in higher dimensions with absolutely continuous measure states
Super-Brownian motions in two or more dimensions, with constant branching rates, are known to have singular measure states. There exist however much more general super-Brownian motions in which the random branching mechanism is determined by a non-negative continuous additive functional \(A\) of the Brownian motion. The main theorem of this paper shows that if certain technical conditions are imposed on \(A\), making the branching rate relatively irregular, then the resulting process has absolutely continuous measure states. The examples given by the authors to illustrate the applicability of the theorem have irregularities in only one coordinate. Such is for instance the case if \(A\) has a branching rate kernel determined along one coordinate by a typical realization of a stable subordinator with suitable index; this ensures that the branching effect is restricted to a dense set of parallel hyperplanes.
scientific article; zbMATH DE number 727282
scientific article