Ergodic process

For broader coverage of this topic, see Ergodicity.

In physics, statistics, econometrics and signal processing, a stochastic process is said to be in an ergodic regime if an observable's ensemble average equals the time average.[1] In this regime, any collection of random samples from a process must represent the average statistical properties of the entire regime. Conversely, a regime of a process that is not ergodic is said to be in non-ergodic regime.[2] A regime implies a time-window of a process whereby ergodicity measure is applied.

  1. ^ Cherstvy, Andrey; Chechkin, Aleksei V; Metzler, Ralf (2013), "Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes", New J. Phys., 15 (8): 083039, arXiv:1303.5533, Bibcode:2013NJPh...15h3039C, doi:10.1088/1367-2630/15/8/083039
  2. ^ Originally due to L. Boltzmann. See part 2 of Vorlesungen über Gastheorie. Leipzig: J. A. Barth. 1898. OCLC 01712811. ('Ergoden' on p. 89 in the 1923 reprint.) It was used to prove equipartition of energy in the kinetic theory of gases