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We consider the extreme value statistics of correlated random variables thatarise from a Langevin equation. Recently, it was shown that the extreme valuesof the Ornstein-Uhlenbeck process follow a different distribution than thoseoriginating from its equilibrium measure, composed of independent andidentically distributed Gaussian random variables. Here, we first focus on thediscretely sampled Ornstein-Uhlenbeck process, which interpolates between thesetwo limits. We show that in the limit of large times, its extreme valuesconverge to those of the equilibrium distribution, instead of those of thecontinuously sampled process. This finding folds for any positive samplinginterval, with an abrupt transition at zero. We then analyze the Langevinequation for any force that gives rise to a stable equilibrium distribution.For forces which asymptotically grow with the distance from the equilibriumpoint, the above conclusion continues to hold, and the extreme values for largetimes correspond to those of independent variables drawn from the equilibriumdistribution. However, for forces which asymptotically decay to zero with thedistance, the discretely sampled extreme value statistics at large timesapproach those of the continuously sampled process.

Discrete sampling of correlated random variables modifies the long-time behavior of their extreme value statistics