ERGODICITY OF NON-STATIONARY RANDOM PROCESSES
Victor V. Nosov, Vladimir P. Lukin, Evgeny V. Nosov, Andrei V. Torgaev · 2025
The ergodic theorem for the case of non-stationary random processes is proved. For stationary processes such theorem was proved by Taylor (1921). This result is important for atmospheric turbulence, in which all hydrodynamic elements are non-stationary and have a pronounced diurnal change and annual variation. The proof confirms the ideas of Reynolds (1894), according to which the time averaging interval should be large compared to the characteristic periods of the pulsation field, but small compared to the periods of the averaged field.