LONG-TIME ASYMPTOTIC OF STABLE DAWSON-WATANABE PROCESSES IN SUPERCRITICAL REGIMES

doi:10.1007/s10473-019-0104-y

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (1): 37-45.doi: 10.1007/s10473-019-0104-y

LONG-TIME ASYMPTOTIC OF STABLE DAWSON-WATANABE PROCESSES IN SUPERCRITICAL REGIMES

Khoa LÊ^1,2

1. Department of Mathematical and Statistical Sciences, University of Alberta, 632 Central Academic, Edmonton, AB T6G 2R3, Canada;
2. Department of Mathematics, South Kensington Campus, Imperial College London, London, SW7 2AZ, United Kingdom

收稿日期:2018-01-12 出版日期:2019-02-25 发布日期:2019-03-13
作者简介:Khoa LÊ,n.le@imperial.ac.uk

LONG-TIME ASYMPTOTIC OF STABLE DAWSON-WATANABE PROCESSES IN SUPERCRITICAL REGIMES

Khoa LÊ^1,2

1. Department of Mathematical and Statistical Sciences, University of Alberta, 632 Central Academic, Edmonton, AB T6G 2R3, Canada;
2. Department of Mathematics, South Kensington Campus, Imperial College London, London, SW7 2AZ, United Kingdom

Received:2018-01-12 Online:2019-02-25 Published:2019-03-13

摘要/Abstract

摘要： 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 -(-△) 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 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.

关键词: Dawson-Watanabe process, α-stable process

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 -(-△) 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 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.

Key words: Dawson-Watanabe process, α-stable process

Khoa LÊ. LONG-TIME ASYMPTOTIC OF STABLE DAWSON-WATANABE PROCESSES IN SUPERCRITICAL REGIMES[J]. 数学物理学报(英文版), 2019, 39(1): 37-45.

Khoa LÊ. LONG-TIME ASYMPTOTIC OF STABLE DAWSON-WATANABE PROCESSES IN SUPERCRITICAL REGIMES[J]. Acta mathematica scientia,Series B, 2019, 39(1): 37-45.

LONG-TIME ASYMPTOTIC OF STABLE DAWSON-WATANABE PROCESSES IN SUPERCRITICAL REGIMES

LONG-TIME ASYMPTOTIC OF STABLE DAWSON-WATANABE PROCESSES IN SUPERCRITICAL REGIMES

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