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SUPER-BROWNIAN MOTIONS WITH ABSOLUTELY CONTINUOUS MEASURE STATES

Suppose X = {Xt,Pμ} is a d-dimensional super-Brownian motion with branching rate function A and general branching mechanism ψ. It discusses conditions on A to guarantee that Xt has absolutely continuous states. For the particular case of ψ(s, x, z) = z2, the analogous problem has been discussed by Dawson and Fleischmann[2]. The author generalizes and simplifies the conditions of Dawson and Fleischmann based on an improvement on their argument.