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<p>We present the first rates of convergence to an <i>N</i>-dimensional Brownian motion when <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(N\ge 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> for discrete and continuous time dynamical systems. Additionally, we provide the first rates for continuous time in any dimension. Our results hold for nonuniformly hyperbolic and expanding systems, such as Axiom A flows, suspensions over a Young tower with exponential tails, and some classes of intermittent solenoids.</p>

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Rates for Maps and Flows in a Deterministic Multidimensional Weak Invariance Principle

  • 期刊论文

  • 发表日期：

    2026年5月2日

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  • Nicolò Paviato

摘要

We present the first rates of convergence to an N-dimensional Brownian motion when \(N\ge 2\) N ≥ 2 for discrete and continuous time dynamical systems. Additionally, we provide the first rates for continuous time in any dimension. Our results hold for nonuniformly hyperbolic and expanding systems, such as Axiom A flows, suspensions over a Young tower with exponential tails, and some classes of intermittent solenoids.