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ASYMPTOTIC BEHAVIOUR OF DENSITIES OF MULTI-DIMENSIONAL STABLE DISTRIBUTIONS

Seiji Hiraba
Tsukuba Journal of Mathematics
Vol. 18, No. 1 (June 1994), pp. 223-246
Stable URL: http://www.jstor.org/stable/43685890
Page Count: 24
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
ASYMPTOTIC BEHAVIOUR OF DENSITIES OF MULTI-DIMENSIONAL STABLE DISTRIBUTIONS
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Abstract

In one-dimension asymptotic behaviour of densities of stable distributions is well-known. However, in multi-dimensional cases it is very difficult to investigate asymptotic behaviour of densities of non-degenerate stable distributions in general. In the present paper we give the following two results: If the Lévy measure of the stable distribution has mass at a half-line, then the density decreases along the half-line with the same order as in one-dimensional case. If the Lévy measure is supported only on finitely many halflines, then we can determine asymptotic behaviour along each direction starting at 0.

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