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arXiv · 2608.21090

Ornstein-Uhlenbeck process conditioned to have restricted $L_2$-norm

Frank Aurzada·Mikhail Lifshits·Max Wiegand
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Abstract

We condition an Ornstein-Uhlenbeck process on having an atypically small $L_2$-norm on long time intervals. The weak limit of these conditioned processes is again an Ornstein-Uhlenbeck process, this time with a stronger mean-reverting force than the unconditioned process, which is controlled by the restriction on the $L_2$-norm.

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Frank Aurzada, Mikhail Lifshits, Max Wiegand. 2026-08-21. Ornstein-Uhlenbeck process conditioned to have restricted $L_2$-norm. https://arxiv.org/abs/2608.21090

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