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Methodologically, we extend the generator comparison approach of Stein's method to piecewise-deterministic Markov processes (PDMPs). The discontinuous nature of the PDMP at jump times necessitates using the basic adjoint relationship (BAR), instead of the infinitesimal generator, to characterize the stationary distribution. A second-order Taylor expansion of the BAR jump terms, coupled with a Palm-inversion step that converts event-averaged quantities into time averages, yields the candidate diffusion generator and a transparent interior/boundary error decomposition. In parallel, we show how the prelimit generator approach -- working with the Poisson equation of the queueing system instead of the diffusion process -- offers a promising avenue for bounding the challenging boundary terms.
From: Anton Braverman [view email]
[v1]
Wed, 17 Jul 2024 16:37:48 UTC (50 KB)
[v2]
Tue, 30 Jul 2024 18:23:10 UTC (54 KB)
[v3]
Tue, 2 Sep 2025 16:32:48 UTC (80 KB)
[v4]
Tue, 30 Jun 2026 17:06:53 UTC (95 KB)
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