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arXiv · 1409.3649

Effects of randomization on asymptotic periodicity of nonsingular transformations

Hiroshi Ishitani·Kensuke Ishitani
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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.

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Hiroshi Ishitani, Kensuke Ishitani. 2014-09-12. Effects of randomization on asymptotic periodicity of nonsingular transformations. https://arxiv.org/abs/1409.3649

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