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Lebesgue approximation of (2,β)-superprocesses

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  • He, Xin

Abstract

Let ξ=(ξt) be a locally finite (2,β)-superprocess in Rd with β<1 and d>2/β. Then for any fixed t>0, the random measure ξt can be a.s. approximated by suitably normalized restrictions of Lebesgue measure to the ε-neighborhoods of suppξt. This extends the Lebesgue approximation of Dawson–Watanabe superprocesses. Our proof is based on a truncation of (α,β)-superprocesses and uses bounds and asymptotics of hitting probabilities.

Suggested Citation

  • He, Xin, 2013. "Lebesgue approximation of (2,β)-superprocesses," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1802-1819.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:5:p:1802-1819
    DOI: 10.1016/j.spa.2013.01.010
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    References listed on IDEAS

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    1. Tribe, Roger, 1994. "A representation for super Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 51(2), pages 207-219, July.
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    Cited by:

    1. Tahir Andrabi & Jishnu Das & Asim Ijaz Khwaja, 2015. "Delivering education: a pragmatic framework for improving education in low-income countries," Chapters, in: Pauline Dixon & Steve Humble & Chris Counihan (ed.), Handbook of International Development and Education, chapter 6, pages 85-130, Edward Elgar Publishing.

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