Time to reach the maximum for a stationary stochastic process.
Time to reach the maximum for a stationary stochastic process.
复制标题
达到平稳随机过程最大值的时间。
作者：
Francesco Mori;S. Majumdar;G. Schehr
We consider a one-dimensional stationary time series of fixed duration T. We investigate the time t_{m} at which the process reaches the global maximum within the time interval [0,T]. By using a path-decomposition technique, we compute the probability density function P(t_{m}|T) of t_{m} 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 P(t_{m}|T) is always symmetric around the midpoint t_{m}=T/2, 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 P(t_{m}|T) becomes universal, i.e., independent of the details of the potential, at late times. This distribution P(t_{m}|T) becomes uniform in the "bulk" 1≪t_{m}≪T and has a nontrivial universal shape in the "edge regimes" t_{m}→0 and t_{m}→T. Some of these results have been announced in a recent letter [Europhys. Lett. 135, 30003 (2021)0295-507510.1209/0295-5075/ac19ee].
We consider a one-dimensional stationary time series of fixed duration T. We investigate the time t_{m} at which the process reaches the global maximum within the time interval [0,T]. By using a path-decomposition technique, we compute the probability density function P(t_{m}|T) of t_{m} 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 P(t_{m}|T) is always symmetric around the midpoint t_{m}=T/2, 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 P(t_{m}|T) becomes universal, i.e., independent of the details of the potential, at late times. This distribution P(t_{m}|T) becomes uniform in the "bulk" 1≪t_{m}≪T and has a nontrivial universal shape in the "edge regimes" t_{m}→0 and t_{m}→T. Some of these results have been announced in a recent letter [Europhys. Lett. 135, 30003 (2021)0295-507510.1209/0295-5075/ac19ee].
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影响因子：
19.6
作者：
Turlier, H.;Fedosov, D. A.;Betz, T.
通讯作者：
Betz, T.
影响因子：
56.9
作者：
Astumian, RD
通讯作者：
Astumian, RD
DOI：
10.1126/science.aac8167
发表时间：
2016-04-29
期刊：
Science (New York, N.Y.)
影响因子：
--
作者：
Battle C;Broedersz CP;Fakhri N;Geyer VF;Howard J;Schmidt CF;MacKintosh FC
通讯作者：
MacKintosh FC
DOI：
10.1088/1742-5468/ab7c5f
发表时间：
2020
期刊：
Journal of Statistical Mechanics: Theory and Experiment
影响因子：
--
作者：
A.K. Hartmann;S.N. Majumdar;H. Schawe;G. Schehr
通讯作者：
G. Schehr