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This article is cited in 5 scientific papers (total in 5 papers)
Short Communications
Asymptotic expansion of the distribution of a homogeneous functional of a strictly stable random vector. II
N. V. Smorodina Saint-Petersburg State University
Abstract:
Let $u$ be a strictly stable non-Gaussian vector with the exponent of stability $\alpha\ge 1$, taking on values in a separable Banach space $B$. Let $h\colon B\to\mathbb R$ be a smooth homogeneous functional and let $F$ be the distribution function of the random variable $h(u)$. For the function $1-F(x)$ we obtain an asymptotic expansion of the form $\sum_{k=1}^n c_kx^{-k\alpha}+O(x^{-(n+1)\alpha})$, $x\to\infty$ ($n$ is determined by the smoothness of $h$). To establish the expansion we use a new approach which is based on the decomposition of the distribution into the sum of linear functionals.
Keywords:
strictly stable distribution, spectral measure, space of configurations, Poisson random measure, linear functional in a Banach space, stochastic integral.
Received: 27.02.1998
Citation:
N. V. Smorodina, “Asymptotic expansion of the distribution of a homogeneous functional of a strictly stable random vector. II”, Teor. Veroyatnost. i Primenen., 44:2 (1999), 458–465; Theory Probab. Appl., 44:2 (2000), 419–427
Linking options:
https://www.mathnet.ru/eng/tvp783https://doi.org/10.4213/tvp783 https://www.mathnet.ru/eng/tvp/v44/i2/p458
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