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Let B be a Banach space, X be a stable B -valued random vector with exponent d∈(0,2), and P(·) be the distribution density of the norm of X. In this paper we study the question of the boundedness of P. In particular, we construct examples of a space B with a symmetric stable vector X with exponent d∈(1,2) with unbounded P and prove that if X is a nondegenerate strictly stable vector with exponent d∈(0,1), then P is bounded.
Original language | English |
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Pages (from-to) | 2810-2817 |
Number of pages | 8 |
Journal | Journal of Soviet Mathematics |
Volume | 43 |
Issue number | 6 |
DOIs | |
State | Published - 1 Dec 1988 |
ID: 43812033