Support properties of super-Brownian motions with spatially dependent branching rate

Yan-Xia Ren

Stochastic Processes and their Applications, 2004, vol. 110, issue 1, 19-44

Abstract: We consider a critical finite measure-valued super-Brownian motion X=(Xt,P[mu]) in , whose log-Laplace equation is associated with the semilinear equation , where the coefficient k(x)>0 for the branching rate varies in space, and is continuous and bounded. Suppose that supp [mu] is compact. We say that X has the compact support property, if for every t>0, and we say that the global support of X is compact if . We prove criteria for the compact support property and the compactness of the global support. If there exists a constant M>0 such that k(x)[greater-or-equal, slanted]exp(-Mx2) as x-->[infinity] then X possesses the compact support property, whereas if there exist constant [beta]>2 such that k(x)[less-than-or-equals, slant]exp(-x[beta]) as x-->[infinity] then X does not have the compact support property. For the global support, we prove that if k(x)=x-[beta] (0[less-than-or-equals, slant][beta]

Keywords: Super-Brownian; motion; Compact; support; property; Global; support; Finite; time; extinction (search for similar items in EconPapers)
Date: 2004
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