Distribution density of the norm of a stable vector

Research output

Abstract

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 languageEnglish
Pages (from-to)2810-2817
Number of pages8
JournalJournal of Soviet Mathematics
Volume43
Issue number6
DOIs
Publication statusPublished - 1 Dec 1988

Scopus subject areas

  • Mathematics(all)

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