arXiv 17 Feb 2024 · Mathematics — Probability · publishedStochastic Processes and their Applications (2026)
arXiv:2402.11394 · PDF · DOI · OpenAlex · Extracted main text
This paper provides a bound for the supremum of sample averages over a class of functions for a general class of mixing stochastic processes with arbitrary mixing rates. Regardless of the speed of mixing, the bound is comprised of a concentration rate and a novel measure of complexity. The speed of mixing, however, affects the former quantity implying a phase transition. Fast mixing leads to the standard root-n concentration rate, while slow mixing leads to a slower concentration rate, its speed depends on the mixing structure. Our findings are applied to derive strong approximation results for a general class of mixing processes with arbitrary mixing rates.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Talagrand, Michel (2014) Upper and Lower Bounds for Stochastic Processes | 0.956 | 16 | 4 | 88% |
| 2 | Doukhan, Paul and Massart, Pascal and Rio, Emmanuel (1995) Invariance principles for absolutely regular empirical processes | 0.953 | 15 | 4 | 87% |
| 3 | Rio, Emmanuel (2017) Asymptotic theory of weakly dependent random processes | 0.874 | 6 | 3 | 67% |
| 4 | Dedecker, Jérôme and Prieur, Clémentine (2005) New dependence coefficients. Examples and applications to statistics | 0.860 | 11 | 4 | 64% |
| 5 | Dedecker, Jérôme and Prieur, Clémentine (2004) Coupling for $ $-dependent sequences and applications | 0.860 | 11 | 3 | 64% |
| 6 | Dedecker, Jérôme and Merlevede, Florence (2006) Inequalities for partial sums of Hilbert-valued dependent sequences and applications | 0.693 | 12 | 2 | 50% |
| 7 | Ramon van Handel (2018) Chaining, interpolation and convexity II: The contraction principle | 0.644 | 3 | 2 | 67% |
| 8 | van der Vaart, Aad W. and Wellner, Jon (1996) Weak Convergence and Empirical Processes with Applications to Statistics | 0.644 | 3 | 2 | 67% |
| 9 | Talagrand, Michel (2005) The Generic Chaining | 0.644 | 2 | 2 | 100% |
| 10 | Yu, Bin (1994) Rates of convergence for empirical processes of stationary mixing sequences | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 25 scored citations.