Osaka Journal of Mathematics

Effects of randomization on asymptotic periodicity of nonsingular transformations

Hiroshi Ishitani and Kensuke Ishitani

Full-text: Open access

Abstract

It is known that the Perron--Frobenius operators of piecewise expanding $\mathcal{C}^2$ transformations possess an asymptotic periodicity of densities. On the other hand, external noise or measurement errors are unavoidable in practical systems; therefore, all realistic mathematical models should be regarded as random iterations of transformations. This paper aims to discuss the effects of randomization on the asymptotic periodicity of densities.

Article information

Source
Osaka J. Math., Volume 54, Number 1 (2017), 37-53.

Dates
First available in Project Euclid: 3 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1488531783

Mathematical Reviews number (MathSciNet)
MR3619747

Zentralblatt MATH identifier
1367.47014

Subjects
Primary: 28D99: None of the above, but in this section
Secondary: 37A30: Ergodic theorems, spectral theory, Markov operators {For operator ergodic theory, see mainly 47A35} 37A40: Nonsingular (and infinite-measure preserving) transformations

Citation

Ishitani, Hiroshi; Ishitani, Kensuke. Effects of randomization on asymptotic periodicity of nonsingular transformations. Osaka J. Math. 54 (2017), no. 1, 37--53. https://projecteuclid.org/euclid.ojm/1488531783


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