A critical spatially homogeneous measure-valued branching process in Rd is studied where the initial state has infinite asymptotic density. In low dimensions d the process becomes locally extinct, in high dimensions it explodes (locally), but in a critical dimension both effects are exhibited.

Stochastic Analysis and Applications
School of Mathematics and Statistics

Dawson, D.A, Fleischmann, K., Foley, R.D., & Peletier, L.A. (1986). A critical measure-valued branching process with infinite mean. Stochastic Analysis and Applications, 4(2), 117–129. doi:10.1080/07362998608809084