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Simultaneous Pointwise Majorization for Mixed Tail Processes with Applications in Gaussian Chaos and Ergodic Diffusions

arXiv · AI, language, vision and robotics · article · Sep 1, 2026 · UTC

Classical chaining controls an indexed stochastic process through a single worst-case bound and can therefore obscure substantial variation across the index set. We develop the first simultaneous pointwise majorization theory for Banach-valued processes with finite-metric mixed-tail increments. Suppose that an anchored process $(Z_t)_{t\in T}$ satisfies, for some integer $m\ge1$, pseudo-metrics $d_1,\ldots,d_m$, and orders $α_1,\ldots,α_m>0$, \begin{align*} \mathbb{P}\{\|Z_t-Z_s\|>\sum_{j=1}^m u^{1/α_j}d_j(s,t)\}\le 2e^{-u},s,t\in T. \end{align*} For ambient priors $μ_1,\ldots,μ_m$, let $v_j(t

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