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

2017/05/31 by Khoa Lê, Lê, Khoa
Mathematics · #60F15 #60G52 #60J68 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60F15 #msc:60G52 #msc:60J68

paper · pdf · doi:10.48550/arxiv.1705.10938

arxiv created 2017/05/31 · arxiv updated 2017/06/01

Abstract

Let W=(W_t)_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)^{\frac α2} satisfying some integrability condition. Assuming the initial measure W₀ 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.

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