Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (6): 1474-1484.

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Properties of Superdiffusions with Singular Branching Mechanism

 ZHANG Jing1,2, REN Yan-Xia2   

  1. 1.School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021;
    2.School of Mathematical Sciences, Peking University, Beijing 100871
  • Received:2008-01-19 Revised:2009-06-09 Online:2010-12-25 Published:2010-12-25
  • Supported by:

    国家自然科学基金(10971003)资助

Abstract:

Suppose X is a superdiffusion on domain DRd, whose underlying motion ζ is a diffusion process with absorption at the boundary corresponding to generator
 

L=12i,j=1dai,j(x)2xixj+i=1dbi(x)xi,

 whose  branching rate function is dt, and branching mechanism is of the form ψ(x, z) =α(x)z2, x ∈D, α∈Cη(D)(0<η≤1), and α(x)≡0 on D0(D0 is a bounded domain in D), α>0 on D\D0. The authors prove criteria for extinction, compact support property and global support being compact.

Key words: Superdiffusion, Extinction, Compact support property, Global support being compact

CLC Number: 

  • 60J80
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