Long run control of nonhomogeneous Markov processes

2025/06/18 by Łukasz Stettner, Stettner, Łukasz
Engineering · #90C40 #93E20 #99J55 #Advanced Control Systems Optimization #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2506.15542

openalex publication_date 2025/06/18 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

Abstract

In the paper average reward per unit time and average risk sensitive reward functionals are considered for controlled nonhomogeneous Markov processes. Existence of solutions to suitable Bellman equations is shown. Continuity of the value functions with respect to risk parameter is also proved. Finally stability of functionals with respect to pointwise convergence of Markov controls is studied.

Citations

• Stability of long run functionals with respect to stationary Markov controls
• Ergodicity of inhomogeneous Markov processes under general criteria
• Discrete-time risk sensitive portfolio optimization with proportional transaction costs

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• Long run stochastic control problems with general discounting
• Stability of long run functionals with respect to stationary Markov controls
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