Brownian motion conditioned to have restricted $L_2$-norm

Frank Aurzada,Mikhail Lifshits, Dominic T. Schickentanz

arxiv（2023）

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摘要

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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