On mixture representation of the Linnik density

Burak Erdogan
Department of Mathematics
Bilkent University
06533 Bilkent
Ankara
Turkey
e-mail: erdogan@fen.bilkent.edu.tr
e-mail: iossif@fen.bilkent.edu.tr
and
I. V. Ostrovskii

Abstract:

Let $p_{\alpha,\theta}$ be the Linnik density, that is, the probability density with the characteristic function
$$\begin{gather*}\varphi_{\alpha,\theta} (t) := 1/(1+e^{i\theta\sgn t}\vert t\vert... ...< 2, \vert\theta\vert\leq \min(\pi \alpha /2,\pi-\pi \alpha /2)\}. \end{gather*}$$
The following problem is studied: Let $(\alpha,\theta)$, $(\beta,\vartheta)$ be two points of PD. When is it possible to represent $p_{\beta,\vartheta}$ as a scale mixture of $p_{\alpha,\theta}$? A subset of the admissible pairs $(\alpha,\theta)$, $(\beta,\vartheta)$ is described.

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© Copyright 1998, Australian Mathematical Society