Osaka Journal of Mathematics

Effects of randomization on asymptotic periodicity of nonsingular transformations

Hiroshi Ishitani and Kensuke Ishitani

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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

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

First available in Project Euclid: 3 March 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


Ishitani, Hiroshi; Ishitani, Kensuke. Effects of randomization on asymptotic periodicity of nonsingular transformations. Osaka J. Math. 54 (2017), no. 1, 37--53.

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