Applications of variable discounting dynamic programming to iterated function systems and related problems. (8th February 2019)

• Record Type: Journal Article
• Authors: Cioletti, L; Oliveira, Elismar R
• Is Part Of: Nonlinearity. Volume 32:Number 3(2019)
• Page Start: 853
• Page End: 883
• Publication Date: 2019-02-08
• Subjects: Bellman–Hamilton–Jacobi equations -- dynamic programming -- thermodynamic formalism -- ergodic theory -- transfer operator -- eigenfunctions; 37AXX -- 37DXX -- 49LXX; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aaf087
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We study existence and uniqueness of the fixed point solutions of a large class of nonlinear variable discounted transfer operators associated to a sequential decision-making process. We establish regularity properties of these solutions, with respect to the immediate return and the variable discount. In addition, we apply our methods to reformulating and solving, in the setting of dynamic programming, some central variational problems on the theory of iterated function systems, Markov decision processes, discrete Aubry–Mather theory, Sinai–Ruelle–Bowen measures, fat solenoidal attractors, and ergodic optimization.