Distributions on the circle group
Articles
Simona Staskevičiūtė
Vytautas Magnus University
Published 2019-04-23
https://doi.org/10.15388/NA.2019.3.7
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Keywords

probability distributions on the unit circle
wrapped lattice and quasi-lattice distributions
Bergström identity on the unit circle

How to Cite

Staskevičiūtė, S. (2019) “Distributions on the circle group”, Nonlinear Analysis: Modelling and Control, 24(3), pp. 433–446. doi:10.15388/NA.2019.3.7.

Abstract

In this paper, we extend the definition of a random angle and the definition of a probability distribution of a random angle. We expand P. Lévy’s researches related to wrapping the probability distributions defined on R. We determine a relation between quasi-lattice probability distributions on R and lattice probability distributions on the unit circle S. We use the Bergström identity for comparison of a convolution of probability distributions of random angles. We also prove an inverse formula for lattice probability distributions on S.

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