Analytic and asymptotic properties of non-symmetric Linnik's probability densities

Analytic and Asymptotic Properties of Generalized Linnik Probability Densities

“…w x right hand side of 11 exist. Similarly to 8,11,15 , it is the case for an uncountable dense subset of EPD. To describe this subset we need Liouville numbers.…”

“…generalized Linnik densities p for any ␣, , g EPD and to obtain ␣ , , w x corresponding generalizations of results of 8, 11 . However, the main w x methods of 8,11 are not applicable to this aim. The fact is that these methods are based on the idea that in the case s 1, the representation Ž .…”

Analytic and Asymptotic Properties of Multivariate Generalized Linnik’s Probability Densities

“…For the special cases where ν = 1 or n = 1, (3.7) was obtained in [6][7][8]23, 50] by different methods. Notice that the large r-asymptotic behavior of q α,ν,n (r) is very different for the case of α ∈ (0, 2) and α = 2. q α,ν,n (r) decays polynomially when α ∈ (0, 2) and exponentially when α = 2.…”

Geometric stable processes and related fractional differential equations

“…is limited to R + and its law coincides, for 0 < α ≤ 1, with the Mittag-Leffler distribution, as shown in [9] and [12]. Moreover the GS distribution is sometimes referred to as "asymmetric Linnik distribution", since it can be considered a generalization of the latter (to which it reduces for β = µ = 0, see [13], [7]). The Linnik distribution exhibits fat tails, finite mean for 1 < α ≤ 2 and also finite variance only for α = 2 (when it takes the name of Laplace distribution) and is applied in particular to model temporal changes in stock prices (see [2]).…”