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

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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.

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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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Authors and Affiliations

  1. Department of Mathematical and Statistical Sciences, University of Alberta, 632 Central Academic, Edmonton, AB, T6G 2R3, Canada

    Khoa Lê

  2. Department of Mathematics, South Kensington Campus, Imperial College London, London, SW7 2AZ, United Kingdom

    Khoa Lê

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  1. Khoa Lê
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Correspondence to Khoa Lê.

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Lê, K. Long-Time Asymptotic of Stable Dawson-Watanabe Processes in Supercritical Regimes. Acta Math Sci 39, 37–45 (2019). https://doi.org/10.1007/s10473-019-0104-y

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  • DOI: https://doi.org/10.1007/s10473-019-0104-y

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