Abstract
We consider a one-dimensional stationary time series of fixed duration . We investigate the time at which the process reaches the global maximum within the time interval . By using a path-decomposition technique, we compute the probability density function of for several processes, that are either at equilibrium (such as the Ornstein-Uhlenbeck process) or out of equilibrium (such as Brownian motion with stochastic resetting). We show that for equilibrium processes the distribution of is always symmetric around the midpoint , as a consequence of the time-reversal symmetry. This property can be used to detect nonequilibrium fluctuations in stationary time series. Moreover, for a diffusive particle in a confining potential, we show that the scaled distribution becomes universal, i.e., independent of the details of the potential, at late times. This distribution becomes uniform in the “bulk” and has a nontrivial universal shape in the “edge regimes” and . Some of these results have been announced in a recent letter [Europhys. Lett. 135, 30003 (2021)].
12 More- Received 27 July 2022
- Accepted 11 October 2022
DOI:https://doi.org/10.1103/PhysRevE.106.054110
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