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Acta Mathematica Scientia

, Volume 39, Issue 1, pp 37–45 | Cite as

Long-Time Asymptotic of Stable Dawson-Watanabe Processes in Supercritical Regimes

  • Khoa LêEmail author
Article

Abstract

Let W = (Wt)t≥0 be a supercritical α-stable Dawson-Watanabe process (with α ∈ (0, 2]) and f be a test function in the domain of −(-Δ)α/2 satisfying some integrability condition. Assuming the initial measure W0 has a finite positive moment, we determine the long-time asymptotic of arbitrary order of Wt(f). In particular, it is shown that the local behavior of Wt in long-time is completely determined by the asymptotic of the total mass Wt(1), a global characteristic.

Key words

Dawson-Watanabe process α-stable process 

2010 MR Subject Classification

60J68 60F15 60G52 

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Notes

Acknowledgements

The author thanks PIMS for its support through the Postdoctoral Training Centre in Stochastics during the completion of the paper.

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Copyright information

© Wuhan Institutes of Physics and Mathematics, Chinese Academy of Sciences 2019

Authors and Affiliations

  1. 1.Department of Mathematical and Statistical SciencesUniversity of Alberta, 632 Central AcademicEdmontonCanada
  2. 2.Department of Mathematics, South Kensington CampusImperial College LondonLondonUnited Kingdom

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