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Teor. Veroyatnost. i Primenen., 2006, Volume 51, Issue 4, Pages 691–711 (Mi tvp20)  

Asymptotic properties of multidimensional stable densities and asymmetric problems of large deviations

A. V. Nagaev

Nikolaus Copernicus University

Abstract: The paper considers asymptotic properties of the so-called asymmetric multidimensional stable distributions with the property that the minimal convex conus generated by a support of Poisson spectral measure does not coincide with $\mathbf R^d$. The density of such a distribution along some directions can decrease extremely quickly. Using methods of the conjugate Cramér distributions we find the exact asymptotic and write an asymptotic series which describes a character of the decrease.

DOI: https://doi.org/10.4213/tvp20

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English version:
Theory of Probability and its Applications, 2007, 51:4, 626–644

Bibliographic databases:

UDC: $\alpha$-stable distribution, strictly $\alpha$-stable distribution, asymmetric stable law, Cram\'er transform, Legendre--Fenchel transform, Poisson spectral measure, conjugate distribution.
Received: 15.09.2004

Citation: A. V. Nagaev, “Asymptotic properties of multidimensional stable densities and asymmetric problems of large deviations”, Teor. Veroyatnost. i Primenen., 51:4 (2006), 691–711; Theory Probab. Appl., 51:4 (2007), 626–644

Citation in format AMSBIB
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