Remarks on the Positivity of Densities of Stable Probability Measure on R(d)
Abstract
Let mu be an index alpha, 0 < alpha < 2, stable prob. measure on R superscript d, the d-Euclidean space. Let sigma be the spectral measure of mu on the boundary of the unit sphere of R superscript d; and assume that the support of sigma is d-dimensional. Using known results about the support of mu, simple proofs are provided for the following two facts about the continuous bounded density f sub mu of mu: (i) If 1 < or = alpha < 2, then f sub mu is positive on R superscript d; (ii) if 0 < alpha < 1, then f mu (x) > 0 if and only if x belongs to the interior of the translated cone a sub 0 + C sub O, where C sub O is the smallest closed cone generated by the support of sigma, and a sub 0 is the centering element of mu.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 26, 1988
- Accession Number
- ADA197920
Entities
People
- Balram S. Rajput
Organizations
- University of Tennessee