math.PR · 2026-09-10 · No. 111

Probability, 2026-09-10.

1 new papers in math.PR. Titles, authors, abstracts. Links to arXiv. Want this in your inbox every morning? Subscribe →

01 — The papers

1 entries
  1. 01

    Gaussian Approximation for Multivariate Martingale Sums from Uniformly Ergodic Markov Chains

    Yixuan Zhang, Qiaomin Xie

    math.PR · cs.LG · stat.ML

    We develop Gaussian approximation bounds in higher-order Wasserstein distance $W_p$, $p\geq2$, for sums of multivariate martingale differences generated by a uniformly ergodic Markov chain. Under an $L^{(2+η)p}$-moment condition with $η>0$, we establish the explicit bound $$ O\left( p^3 \|A\|_4^2 + pd^{1/4}\|A\|_2^{1/2}\|A\|_4^2 \right) $$ where $A\in\mathbb{R}^n$ collects the $L^{(2+η)p}$-sizes of the $n$ individual martingale increments. In...

    arxiv.org/abs/2609.09480 · PDF

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