Approximation of Multidimensional Stable Densities

By T. Byczkowski, John P. Nolan, B. Rajput. 1993

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Characteristic Kernels and Infinitely Divisible Distributions (2014, background): “…distribution on Rd can be approximated arbitrarily well by another α-stable distribution with a discrete spectral measure Γd, i.e., the class of αstable distributions with discrete spectral measures Γd is dense in the set of all the α-stable distributions (Byczkowski et al., 1993, Theorem 1).”
Multivariate elliptically contoured stable distributions: theory and estimation (2013, background): “Byczkowski et al. (1993) and Abdul-Hamid and Nolan (1998) give expressions for general multivariate stable densities.”
Portfolio Modeling with Heavy Tailed Random Vectors (2003, methodology): “If M is discrete with M(θi) = pi, then it follows from the characteristic function formulas that Y can be represented as the sum of independent stable components laid out along the θi directions, and the methods of Nolan [56, 59] can be used to plot multivariable stable densities, see Byczkowski, No”
Regularity theory for general stable operators (2014, methodology): “Stable processes can be used to model real-world phenomena [32, 20], and in particular they are commonly used in Mathematical Finance; see for example [26, 11, 27, 28, 29, 8] and references therein.”