Necessary and sufficient conditions for a solution to the risk-sensitive Poisson equation on a finite state space

DOI10.1016/j.sysconle.2008.11.001zbMath1159.93030OpenAlexW1975978639MaRDI QIDQ1015761

Daniel Hernández-Hernández, Rolando Cavazos-Cadena

Publication date: 30 April 2009

Published in: Systems \& Control Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.sysconle.2008.11.001

zbMATH Keywords

hitting timemultiplicative Poisson equationconstant average costunichain propertyunique recurrent class

Mathematics Subject Classification ID

Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Stochastic systems in control theory (general) (93E03)

Related Items (6)

Unnamed Item ⋮ Convergence of value functions for finite horizon Markov decision processes with constraints ⋮ Infinite horizon risk-sensitive control of diffusions without any blanket stability assumptions ⋮ Poisson equations associated with a homogeneous and monotone function: necessary and sufficient conditions for a solution in a weakly convex case ⋮ Phase Transitions for Controlled Markov Chains on Infinite Graphs ⋮ Solutions of the average cost optimality equation for finite Markov decision chains: Risk-sensitive and risk-neutral criteria

Cites Work

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• Average optimality for risk-sensitive control with general state space
• A system of Poisson equations for a nonconstant Varadhan functional on a finite state space
• Risk-Sensitive Control of Discrete-Time Markov Processes with Infinite Horizon
• Risk-Sensitive Markov Decision Processes
• Risk-Sensitive Optimal Control for Markov Decision Processes with Monotone Cost

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