On finite convolutions of singular distributions and a “singular analog” of the Jessen-Wintner theorem

  • M. V. Pratsiovytyi

Abstract

We study the fractal properties of a convolution of two Cantor distributions. By using the method of characteristic functions, we establish sufficient conditions for the singularity of the convolution of an arbitrary finite number of distributions of random variables with independent s-adic digits. We disprove the hypothesis on the validity of a “singular analog” of the Jessen-Wintner theorem for anomalously fractal distributions.
Published
25.08.1998
How to Cite
Pratsiovytyi, M. V. “On Finite Convolutions of Singular Distributions and a ‘singular analog’ of the Jessen-Wintner Theorem”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 50, no. 8, Aug. 1998, pp. 1082–1088, https://umj.imath.kiev.ua/index.php/umj/article/view/4857.
Section
Research articles