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<p>The theory of random Banach walk in the unit ball in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(l^{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>l</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> (see Banek in J Theor Probab 29:1728–1735, 2016) is modified to take into account the specific needs of noise acoustics. The state-space is now taken to be a ball in the Banach space of sequences with finite energy per unit time, rather than total energy, as in Banek (2016). We call the space <i>noisy</i> and prove an ergodic theorem in it. Furthermore, we show that the popular noise formula used in environmental pollution diagnostics is asymptotically invariant and asymptotically accurate in this noise space.</p>

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Banach Random Walk in Acoustics

  • 期刊论文

  • 发表日期：

    2025年10月31日

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  • Tadeusz Henryk Banek

摘要

The theory of random Banach walk in the unit ball in \(l^{2}\) l 2 (see Banek in J Theor Probab 29:1728–1735, 2016) is modified to take into account the specific needs of noise acoustics. The state-space is now taken to be a ball in the Banach space of sequences with finite energy per unit time, rather than total energy, as in Banek (2016). We call the space noisy and prove an ergodic theorem in it. Furthermore, we show that the popular noise formula used in environmental pollution diagnostics is asymptotically invariant and asymptotically accurate in this noise space.