Solutions of the Multivariate Inverse Frobenius–Perron Problem

Autor:	Colin Fox, Li-Jen Hsiao, Jeong-Eun (Kate) Lee
Jazyk:	angličtina
Rok vydání:	2021
Předmět:	inverse Frobenius–Perron problem Rosenblatt transformation uniform map multivariate probability distribution transfer operator ergodic map Science Astrophysics QB460-466 Physics QC1-999
Zdroj:	Entropy, Vol 23, Iss 7, p 838 (2021)
Druh dokumentu:	article
ISSN:	23070838 1099-4300
DOI:	10.3390/e23070838
Popis:	We address the inverse Frobenius–Perron problem: given a prescribed target distribution ρ, find a deterministic map M such that iterations of M tend to ρ 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.
Databáze:	Directory of Open Access Journals
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