Lebesgue approximation of (2, beta)-superprocesses

作者：He Xin^*

来源：Stochastic Processes and Their Applications, 2013, 123(5): 1802-1819.

DOI：10.1016/j.spa.2013.01.010

• Super-Brownian motion
• Branching mechanism
• Symmetric stable process
• Historical cluster
• Hitting probability
• Hitting bound
• Hitting asymptotic
• Local finiteness
• Local extinction
• Neighborhood measure

Let xi = (xi(t)) be a locally finite (2, beta)-superprocess in R-d with beta %26lt; 1 and d %26gt; 2/beta. Then for any fixed t %26gt; 0, the random measure xi(t) can be a.s. approximated by suitably normalized restrictions of Lebesgue measure to the epsilon-neighborhoods of supp xi(t). This extends the Lebesgue approximation of Dawson-Watanabe superprocesses. Our proof is based on a truncation of (alpha, beta)-superprocesses and uses bounds and asymptotics of hitting probabilities.

• 出版日期2013-5