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Contents of PMS, Vol. 19, Fasc. 2,
pages 375 - 388
 

POINT REGULARITY OF p -STABLE DENSITY IN RD  AND FISHER INFORMATION

Maciej Lewandowski

Abstract: In the paper we prove that the n -th directional derivative of a p -stable density f(x) in the direction a can be estimated by

  n        C(u)     (1-u)[p/(1+p)]
|D af(x)|< 1+-|x|[f(x)]          ,
where 0 < u < 1, and C depends also on geometrical properties of the Lévy measure. This inequality helps us to calculate the Fisher information of stable measures.

1991 AMS Mathematics Subject Classification: Primary -; Secondary -;

Key words and phrases: -

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