A1 Refereed original research article in a scientific journal
Ergodic control of diffusions with random intervention times
Authors: Saarinen Harto, Lempa Jukka
Publisher: CAMBRIDGE UNIV PRESS
Publication year: 2021
Journal: Journal of Applied Probability
Journal name in source: JOURNAL OF APPLIED PROBABILITY
Journal acronym: J APPL PROBAB
Article number: PII S0021900220000807
Volume: 58
Issue: 1
First page : 1
Last page: 21
Number of pages: 21
ISSN: 0021-9002
eISSN: 1475-6072
DOI: https://doi.org/10.1017/jpr.2020.80
Web address : https://www.cambridge.org/core/journals/journal-of-applied-probability/article/abs/ergodic-control-of-diffusions-with-random-intervention-times/3D9F3F2E263C50FEDB8DB94FBA5565C7
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/53665205
We study an ergodic singular control problem with constraint of a regular one-dimensional linear diffusion. The constraint allows the agent to control the diffusion only at the jump times of an independent Poisson process. Under relatively weak assumptions, we characterize the optimal solution as an impulse-type control policy, where it is optimal to exert the exact amount of control needed to push the process to a unique threshold. Moreover, we discuss the connection of the present problem to ergodic singular control problems, and illustrate the results with different well-known cost and diffusion structures.
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