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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 24, Fasc. 2,
pages 367 - 379
 

COMPARISON OF TAIL PROBABILITIES OF STRICTLY SEMISTABLE/STABLE RANDOM VECTORS AND THEIR SYMMETRIZED COUNTERPARTS WITH APPLICATION

Balram S. Rajput
Kavi Rama-Murthy

Abstract: It is shown that the tail probabilities of a strictly (r,a) -semistable (0 < r < 1, 0 < a < 2, a /= 1 ) Banach space valued random vector X and its symmetrized counterpart are ”uniformly” comparable in the sense that the constants appearing in the inequalities depend only on r and a (and not on X or the Banach space). Using this and some other known facts, several corollaries related to the moment inequalities of the random vector X and its symmetrized counterpart are obtained. The corresponding results for strictly a -stable Banach space valued random vectors, a /= 1 , are also derived and discussed.

2000 AMS Mathematics Subject Classification: Primary 60E07, 60E15, 60B11; Secondary 60G50, 60G52.

Key words and phrases: Stable, semistable, inequality.

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