Brownian motion conditioned to have restricted $L_2$-norm

Frank Aurzada; Mikhail Lifshits; Dominic T. Schickentanz

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arXiv · 2312.12982

Brownian motion conditioned to have restricted $L_2$-norm

Frank Aurzada·Mikhail Lifshits·Dominic T. Schickentanz

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Abstract

We condition a Brownian motion on having an atypically small $L_2$-norm on a long time interval. The obtained limiting process is a non-stationary Ornstein-Uhlenbeck process.

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Frank Aurzada, Mikhail Lifshits, Dominic T. Schickentanz. 2024-09-02. Brownian motion conditioned to have restricted $L_2$-norm. https://arxiv.org/abs/2312.12982

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