Aging arcsine law in Brownian motion and its generalization
arXiv:2004.00808 · doi:10.1103/PhysRevE.102.032103
Abstract
Classical arcsine law states that fraction of occupation time on the positive or the negative side in Brownian motion does not converge to a constant but converges in distribution to the arcsine distribution. Here, we consider how a preparation of the system affects the arcsine law, i.e., aging of the arcsine law. We derive aging distributional theorem for occupation time statistics in Brownian motion, where the ratio of time when measurements start to the measurement time plays an important role in determining the shape of the distribution. Furthermore, we show that this result can be generalized as aging distributional limit theorem in renewal processes.
arXiv comment7 pages, 3 figures
References in corpus (18)
- Lévy walks
- Random Time-Scale Invariant Diffusion and Transport Coefficients
- Statistical Aging and Non Ergodicity in the Fluorescence of Single Nanocrystals
- Nonergodic Subdiffusion from Brownian Motion in an Inhomogeneous Medium
- Non-ergodic Intensity Correlation Functions for Blinking Nano Crystals
- Origin of subdiffusion of water molecules on cell membrane surfaces
- Nonergodisity of a time series obeying Lévy statistics
- Safe Leads and Lead Changes in Competitive Team Sports
- Generalized arcsine laws for fractional Brownian motion
- Distributional Response to Biases in Deterministic Superdiffusion
- Aging generates regular motions in weakly chaotic systems
- Distributional Ergodicity in Stored-Energy-Driven Lévy Flights
- Generalized Arcsine Law and Stable Law in an Infinite Measure Dynamical System
- Anomalous diffusion in a quenched-trap model on fractal lattices
- Phase Diagram in Stored-Energy-Driven Lévy Flight
- Subexponential instability implies infinite invariant measure
- Arcsine Laws in Stochastic Thermodynamics
- Distributional behavior of time averages of non- observables in one-dimensional intermittent maps with infinite invariant measures
Cited by in corpus (4)
- Arcsine Law and Multistable Brownian Dynamics in a Tilted Periodic Potential
- Extremal statistics for a resetting Brownian motion before its first-passage time
- Experimental verification of Arcsine laws in mesoscopic non-equilibrium and active systems
- Extremal statistics for a one-dimensional Brownian motion with a reflective boundary