Some Local Approximations of Dawson – Watanabe

نویسندگان

  • Olav Kallenberg
  • O. KALLENBERG
چکیده

Let ξ be a Dawson–Watanabe superprocess in R such that ξt is a.s. locally finite for every t ≥ 0. Then for d ≥ 2 and fixed t > 0, the singular random measure ξt can be a.s. approximated by suitably normalized restrictions of Lebesgue measure to the ε-neighborhoods of supp ξt. When d ≥ 3, the local distributions of ξt near a hitting point can be approximated in total variation by those of a stationary and self-similar pseudo-random measure ξ̃. By contrast, the corresponding distributions for d= 2 are locally invariant. Further results include improvements of some classical extinction criteria and some limiting properties of hitting probabilities. Our main proofs are based on a detailed analysis of the historical structure of ξ.

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تاریخ انتشار 2008