Hamidou Tembine, Tyrone E. Duncan, Bozenna Pasik-Duncan (2025), arXiv preprint (comments: “Presented at IEEE SysCon’2025”) — ARXIV-2506.08025
Key takeaways
- Replacing Rosenblatt noise (non-Gaussian, self-similar, long-range dependent) with Brownian, fractional-Brownian or jump noise before optimising yields suboptimal controllers. The authors derive the Rosenblatt-driven LQ optimal gain via a modified algebraic Riccati equation, and extend the analysis to zero-sum saddle points, non-zero-sum Nash equilibria and mean-field-type games.
Seeded from the abstract and a skim, before the reading in NOTE-068. What follows is what the work says about itself.
The paper brings Rosenblatt noise into stochastic systems, control and mean-field-type game theory to address the limits of Gaussian and Markovian models. It cites real-data evidence of skew, heavy tails and long-range dependence in water demand, e-commerce, power grids, wireless channels and agricultural supply chains. The Rosenblatt process, non-Gaussian, non-Markovian and self-similar, is offered as a baseline model for such behaviour. The authors develop stochastic-calculus formulas for it, apply them to dynamical systems and optimal control, and show that conventional noise approximation is suboptimal. They then give saddle-point conditions for zero-sum games and state-feedback Nash equilibria for non-zero-sum games, and argue that this matters for prediction and control.
Standing in the record
Filed from the survey of 2026-09-25 of work the anthology set aside as out of scope (tier C): 330 seconds of active reading over 2 sessions in the papers-feed tracker. It was filed Deferred, unread. NOTE-068 is the close reading of 2026-09-25, and it placed the work: Rejected — not worth a reader’s time. The control-theoretic results are earlier papers’ (its refs [43]–[46]) restated. Its central new claim, that Gaussian and fBM surrogates give suboptimal control, is false for fBM with matching H, since the costs depend only on covariance. Its empirical sections are unsourced vignettes: numbers without references, “Rosenblatt shape” fits without any fitting procedure, and data from the first author’s own startups. Its ML claim is an assertion with no model or experiment. A reader wanting Rosenblatt-noise LQ control should go to Čoupek–Duncan–Maslowski–Pasik-Duncan (CDC 2018, ref [43]) and Čoupek–Duncan–Pasik-Duncan (SPA 2022, ref [27]).
When seeded, before the reading in NOTE-068, the entry gave a priority for a deeper reading: low — Owner time is moderate (t=330, n=2). The skim captures the structure, and the anthology-relevant ML claim is unsupported, so a deeper read would mainly be to confirm that.
What the seeding asked a deeper reading to check (NOTE-068 is that reading):
- A real point: optimising under a mis-specified noise model is suboptimal. The LQ Riccati modification is concrete and checkable.
- The ML-facing claim about super-diffusion transformers is unsupported in the text I read and should not be cited as evidence. Check whether any later version or the Springer chapter adds experiments.
- The data section is illustrative. Check whether any Rosenblatt fit is actually estimated against alternatives (e.g. stable, or other Hermite processes).
Access when seeded: arXiv abs page (v1 29 May 2025; 47 pp., 17 figures, “Presented at IEEE SysCon’2025”) and full PDF v1 read directly: abstract and index terms, the PDF outline, §III (definition of the Rosenblatt process), the §VI LQ control result and “noise approximation” subsection (p. 26), and pp. 44 (§XIV C and §XV conclusion). A Crossref search found a 2026 Springer chapter, “Mean-Field-Type Games Driven by Rosenblatt Noises”, in Mean-Field-Type Game Theory I. It may be a related version, but I did not open it or confirm its authors, so treat it as unverified.