Non-linear superprocesses

Distribution and Propagation Properties of Superprocesses with General Branching Mechanisms

A theorem of Evans and Perkins (1991) on the absolute continuity of distributions of Dawson-Watanabe superprocesses is extended to general branching mechanisms. This result is then used to establish the propagation properties of the superprocesses following Evans and Perkins (1991) and Perkins (1990).

Immigration Superprocesses with Dependent Spatial Motion and Non-critical Branching

A super - stable motion with infinite mean branching ✩

A class of finite measure-valued càdlàg superprocesses X with Neveu’s (1992) continuous-state branching mechanism is constructed. To this end, we start from certain supercritical (α, d,β)-superprocesses X(β) with symmetric α-stable motion and (1+β)-branching and prove convergence on path space as β ↓ 0. The log-Laplace equation related to X has the locally non-Lipschitz function u logu as non-l...

Conditional Excursion Representation for a Class of Interacting Superprocesses

A class of interacting superprocesses, called superprocesses with dependent spatial motion (SDSMs), has been introduced and characterized in Wang [22] and Dawson et al. [7]. In this paper, we give a construction or an excursion representation of the non-degenerate SDSM with immigration by making use of a Poisson system associated with the conditional excursion laws of the SDSM. As pointed out i...

Hölder Index for Density States of (α, 1, Β)-superprocesses at a given Point

A Hölder regularity index at given points for density states of (α, 1, β)-superprocesses with α > 1 + β is determined. It is shown that this index is strictly greater than the optimal index of local Hölder continuity for those density states.