Long-Time Asymptotic of Stable Dawson-Watanabe Processes in Supercritical Regimes
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 wordsDawson-Watanabe process α-stable process
2010 MR Subject Classification60J68 60F15 60G52
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The author thanks PIMS for its support through the Postdoctoral Training Centre in Stochastics during the completion of the paper.
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