Solutions of the Multivariate Inverse Frobenius–Perron Problem

Entropy

Colin Fox¹  Jeong-Eun (Kate) Lee²  Li-Jen Hsiao³ 

[1] Department of Physics, University of Otago, Dunedin 9016, New Zealand;Department of Statistics, The University of Auckland, Auckland 1010, New Zealand;System Manufacturing Center, National Chung-Shan Institute of Science & Technology, New Taipei City 237209, Taiwan;

关键词: inverse Frobenius–Perron problem;    Rosenblatt transformation;    uniform map;    multivariate probability distribution;    transfer operator;    ergodic map;   

DOI  :  10.3390/e23070838

来源: DOAJ

【 摘 要 】

We address the inverse Frobenius–Perron problem: given a prescribed target distribution $\rho$, find a deterministic map M such that iterations of M tend to $\rho$ in distribution. We show that all solutions may be written in terms of a factorization that combines the forward and inverse Rosenblatt transformations with a uniform map; that is, a map under which the uniform distribution on the d-dimensional hypercube is invariant. Indeed, every solution is equivalent to the choice of a uniform map. We motivate this factorization via one-dimensional examples, and then use the factorization to present solutions in one and two dimensions induced by a range of uniform maps.

【 授权许可】

Unknown