A1 Refereed original research article in a scientific journal
A Note on Asymptotics Between Singular and Constrained Control Problems of One-Dimensional Diffusions
Authors: Saarinen Harto, Lempa Jukka
Publisher: SPRINGER
Publication year: 2022
Journal: Acta Applicandae Mathematicae
Journal name in source: ACTA APPLICANDAE MATHEMATICAE
Journal acronym: ACTA APPL MATH
Article number: 13
Volume: 181
Issue: 1
Number of pages: 17
ISSN: 0167-8019
eISSN: 1572-9036
DOI: https://doi.org/10.1007/s10440-022-00530-w
Web address : https://link.springer.com/article/10.1007/s10440-022-00530-w
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/176690885
We study the asymptotic relations between certain singular and constrained control problems for one-dimensional diffusions with both discounted and ergodic objectives. In the constrained control problems the controlling is allowed only at independent Poisson arrival times. We show that when the underlying diffusion is recurrent, the solutions of the discounted problems converge in Abelian sense to those of their ergodic counterparts. Moreover, we show that the solutions of the constrained problems converge to those of their singular counterparts when the Poisson rate tends to infinity. We illustrate the results with drifted Brownian motion and Ornstein-Uhlenbeck process.
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