 Diffusive limit approximation of pure jump optimal ergodic control problemsMarc Abeille, Bruno Bouchard and Lorenzo Croissant Stochastic Processes and their Applications, 2025, vol. 181, issue C Abstract: Motivated by the design of fast reinforcement learning algorithms, see (Croissant et al., 2024), we study the diffusive limit of a class of pure jump ergodic stochastic control problems. We show that, whenever the intensity of jumps ɛ−1 is large enough, the approximation error is governed by the Hölder regularity of the Hessian matrix of the solution to the limit ergodic partial differential equation and is, indeed, of order ɛγ2 for all γ∈(0,1). This extends to this context the results of Abeille et al. (2023) obtained for finite horizon problems. Using the limit as an approximation, instead of directly solving the pre-limit problem, allows for a very significant reduction in the numerical resolution cost of the control problem. Additionally, we explain how error correction terms of this approximation can be constructed under appropriate smoothness assumptions. Finally, we quantify the error induced by the use of the Markov control policy constructed from the numerical finite difference scheme associated to the limit diffusive problem, which seems to be new in the literature and of independent interest. Date: 2025 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:181:y:2025:i:c:s0304414924002448 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2024.104536 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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