Impulse control maximising average cost per unit time: a non-uniformly ergodic case

TL;DR

This paper studies maximisation of an average-cost-per-unit-time ergodic functional over impulse strategies controlling a Feller-Markov process and shows that the optimal value does not depend on the initial state and provide optimal or $\ve$-optimal strategies.

Abstract

This paper studies maximisation of an average-cost-per-unit-time ergodic functional over impulse strategies controlling a Feller-Markov process. The uncontrolled process is assumed to be ergodic but, unlike the extant literature, the convergence to invariant measure does not have to be uniformly geometric in total variation norm; in particular, we allow for non-uniform geometric or polynomial convergence. Cost of an impulse may be unbounded, e.g., proportional to the distance the process is shifted. We show that the optimal value does not depend on the initial state and provide optimal or $\ve$-optimal strategies.

Theorems & Definitions (61)

• Lemma 2.1
• proof
• Lemma 2.2
• proof
• Lemma 3.1
• proof
• Lemma 3.2
• proof
• Theorem 3.3
• proof