Long-time asymptotic of stable Dawson-Watanabe processes in supercritical regimes

DOI10.1007/S10473-019-0104-YzbMATH Open1499.60279arXiv1705.10938OpenAlexW2963168718MaRDI QIDQ2150703

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Publication date: 30 June 2022

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Abstract: Let $W=(W_t{)}_{tge0}$ be a supercritical $alpha$-stable Dawson-Watanabe process (with $alphain(0,2]$) and $f$ be a test function in the domain of $-(-Delta{)}^{fracalpha2}$ satisfying some integrability condition. Assuming the initial measure $W_0$ has a finite positive moment, we determine the long-time asymptotic of all orders of $W_t(f)$. In particular, it is shown that the local behavior of $W_t$ in long-time is completely determined by the asymptotic of the total mass $W_t(1)$, a global characteristic.

Full work available at URL: https://arxiv.org/abs/1705.10938

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