Asymptotic expansion of the distribution of a homogeneous functional of a strictly stable random vector. II (Q2711134)
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| English | Asymptotic expansion of the distribution of a homogeneous functional of a strictly stable random vector. II |
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2 May 2001
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strictly stable distribution
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spectral measure
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space of configurations
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Poisson random measure
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linear functional in a Banach space
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stochastic integral
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Asymptotic expansion of the distribution of a homogeneous functional of a strictly stable random vector. II (English)
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[For part I see ibid. 41, No. 1, 91-115 (1996); resp. ibid. 41, No. 1, 133-163 (1996; Zbl 0888.60018).]NEWLINENEWLINENEWLINEThe present paper offers asymptotic expansion at infinity for strictly stable non-Gaussian random variables on Banach spaces \(B\) with index \(\alpha\geq 1\) of stability. The object under consideration is the tail behaviour of the distribution of a real smooth homogeneous functional \(h: B\to \mathbb{R}\). The method of proof is based on a Poisson point process approximation of the stable law. This reflects the fact that stable distribution functions are not known but their Lévy measures have an explicit form.
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