A continuous super-Brownian motion in a super-Brownian medium

A continuous super-Brownian motion #CHI#"#rho# is constructed in which branching occurs only in the presence of catalysts which evolve themselves as a continuous super-Brownian motion #rho#. More precisely, the collision local time L[W,#rho#] (in the sense of Barlow et al. [BEP91]) of an underlying Brownian motion path W with the catalytic mass process #rho# governs the branching (in the sense of Dynkin's additive functional approach). In the one-dimensional case, a new type of limit behavior is encountered: the total mass process converges to a limit without loss of expectation mass (persistence) and with a positive (finite) limiting variance, whereas starting with a Lebesgue measure l, stochastic convergence to l occurs. (orig.)SIGLEAvailable from TIB Hannover: RR 5549(165)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman