Multivariate Stable Distributions and Generating Densities

Applied Mathematics Letters, Volume 26, Issue 3, March 2013, Pages 324-329

The probability density function of multivariate stable distributions only applies to special accessible cases. Consequently, because of the absence of an explicit solution for their probability distribution function, applications have been limited. In this paper, we present an analytic method for generating densities to resolve this problem. Some examples and special cases are discussed.

Keywords: Stable distributions, Fractional calculus, Hill–Yosida theorem, Generating densities