We obtain exact almost-sure estimates for the short-time propagation of the closed support of (2, d, β)-superprocesses. Upper estimates are derived by solving a certain singular non-linear evolution equation, whereas lower estimates are obtained by the use of the branching-particle-system approximation.

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Stochastic Processes and their Applications
School of Mathematics and Statistics

Dawson, D.A, & Vinogradov, V. (Vladimir). (1994). Almost-sure path properties of (2, d, β)-superprocesses. Stochastic Processes and their Applications, 51(2), 221–258. doi:10.1016/0304-4149(94)90043-4