Abstract
We study the angular process related to random walks in the Euclidean and in the non-Euclidean space where steps are Cauchy distributed. This leads to different types of nonlinear transformations of Cauchy random variables which preserve the Cauchy density. We give the explicit form of these distributions for all combinations of the scale and the location parameters. Continued fractions involving Cauchy random variables are analyzed. It is shown that the n-stage random variables are still Cauchy distributed with parameters related to Fibonacci numbers. This permits us to show the convergence in distribution of the sequence to the golden ratio.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.