Asymptotic distribution of the derivative of the taut string accompanying Wiener process

2024/11/07 by Mikhail Lifshits, Lifshits, Mikhail, Andrei Podchishchailov +1 · 1 citation
Mathematics · Physics and Astronomy · #advanced mathematical theories #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2411.04690

Abstract

In the article, we find the asymptotic distribution of the derivative of the taut string accompanying a Wiener process in a strip of fixed width on long time intervals. This enables to find explicit expressions for minimal energy (averaged function of the derivative) of an absolutely continuous function in this strip. For example, for kinetic energy which was considered earlier by Lifshits and Setterqvist, the minimal energy per unit of time tends to π²/6r² where r is the strip width.

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• On the minimal integral energy of majorants of the Wiener process

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