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

Frank Aurzada; Mikhail Lifshits; Max Wiegand

paper

Ornstein-Uhlenbeck process conditioned to have restricted $L_{2}$ -norm

arXiv:2608.21090

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.

29 pages

Ornstein-Uhlenbeck process conditioned to have restricted L2​-norm

Abstract

Ornstein-Uhlenbeck process conditioned to have restricted $L_{2}$ -norm