The Failure of the Ergodic Assumption

Details The Failure of the Ergodic Assumption The Failure of the Ergodic Assumption

2010-01-22

arxiv.org/abs/1001.4103v1

Physics

Data Analysis, Statistics and Probability

Scientific paper

The well established procedure of constructing phenomenological ensemble from a single long time series is investigated. It is determined that a time series generated by a simple Uhlenbeck-Ornstein Langevin equation is mean ergodic. However the probability ensemble average yields a variance that is different from that determined using the phenomenological ensemble (time average). We conclude that the latter ensemble is often neither stationary nor ergodic and consequently the probability ensemble averages can misrepresent the underlying dynamic process.

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