Effects of randomization on asymptotic periodicity of nonsingular transformations
Abstract
It is known that the Perron--Frobenius operators of piecewise expanding C2 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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