On the policy improvement algorithm for ergodic risk-sensitive control. Issue 4 (August 2021)

• Record Type: Journal Article
• Authors: Arapostathis, Ari; Biswas, Anup; Pradhan, Somnath
• Is Part Of: Proceedings. Volume 151:Issue 4(2021)
• Page Start: 1305
• Page End: 1330
• Publication Date: 2021-08
• Subjects: Principal eigenvalue -- semilinear differential equations -- stochastic representation -- policy improvement; 35P30 -- 93E20 -- 60J60; Mathematics -- Periodicals; 510
• DOI: 10.1017/prm.2020.61
• Languages: English
• ISSNs: 0308-2105

Abstract

Abstract : In this article we consider the ergodic risk-sensitive control problem for a large class of multidimensional controlled diffusions on the whole space. We study the minimization and maximization problems under either a blanket stability hypothesis, or a near-monotone assumption on the running cost. We establish the convergence of the policy improvement algorithm for these models. We also present a more general result concerning the region of attraction of the equilibrium of the algorithm.