Nonlinear Theory and Its Applications, IEICE
Online ISSN : 2185-4106
ISSN-L : 2185-4106
Special Issue on Random/Pseudorandom Numbers
Ergodic transformations on R preserving Cauchy laws
Ken Umeno
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2016 Volume 7 Issue 1 Pages 14-20

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Abstract

We consider a family of ergodic transformations on the real line R preserving Cauchy laws. A dualistic nature between the ergodic transformation and the associated transformation of the scale parameter of a Cauchy law is proven to be hold, which provides a systematic view of explicit mixing property with the ergodic transformation having the Cauchy law as the limiting distribution.

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© 2016 The Institute of Electronics, Information and Communication Engineers
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