Vol. 26, issue 08, article # 10

Nosov V.V., Lukin V.P. Method of measurement of the turbulence characteristics from the flutter of the astronomical images on the aircraft board. Part 1. Main ergodic theorems. // Optika Atmosfery i Okeana. 2013. V. 26. No. 08. P. 679-691 [in Russian].
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Aspects are investigated of building the statistical characteristics of random functions for discrete-continuous averaging according to the end-time response of the measurement device. This averaging is typically implemented in practice, and any discrete sequence (empirical values of a random function) is partially averaged sequence (over some interval of the argument). Estimates of the rate of convergence are found of the time-mean to the ensemble-mean (the generalizations of the Taylor ergodic theorem). These estimates provide a convergence in probability. It is shown that the convergence rate depends on the integral correlation scales of the random function. These scales are determined by the type of averaging, they are different for the continuous, discrete, and discrete-continuous averaging. An equation relating the correlation functions of non-averaged and partially-averaged random processes is found. It is found that correlation function of the non-averaged process can be satisfactorily recovered from a partially-averaged data, even at very long intervals of partial averaging.


respiratory system, leak tightness of surgical suture, sulfur hexafluoride, laser photoacoustic leak detector


1. Taylor G.I. Diffusion by continuous movements // Proc. London Math. Soc. 1921. V. 20, N 2. P. 196–211.
2. Kolmogorov A.N. Osnovnye ponjatija teorii verojatnostej. M.: Nauka, 1974. 121 p.
3. Prohorov Ju.V., Rozanov Ju.A. Teorija verojatnostej (osnovnye ponjatija, predel'nye teoremy, sluchajnye processy). Izd. 2. M.: Nauka, 1973. 498 p.
4. Monin A.S., Jaglom A.M. Statisticheskaja gidromehanika. V. 1. M.: Nauka, 1967. 696 s.; V. 2. SPb.: Gidrometeoizdat, 1996. 742 p.
5. Tatarskij V.I. Rasprostranenie voln v turbulentnoj atmosfere. M.: Nauka, 1967. 548 с.
6. Lukin V.P., Nosov E.V., Fortes B.V. The efficient outer scale of atmospheric turbulence // Atmos. and Ocean. Opt. 1997. V. 10, N 2. P. 100–109.
7. Fortes B.V., Lukin V.P. Modeling of the imade observed through the turbulent atmosphere // Proc. SPIE. 1992. V. 1668. P. 477–488.
8. Lukin V.P. Opticheskie izmerenija vneshnego masshtaba atmosfernoj turbulentnosti // Optika atmosf. i okeana. 1992. V. 5, N 4. V. 354–377.
9. Lukin V.P. Issledovanie osobennostej struktury krupnomasshtabnoj atmosfernoj turbulentnosti // Optika atmosf. i okeana. 1992. V. 5, N 12. P. 1294–1304.
10. Nosov V.V., Emaleev O.N., Lukin V.P., Nosov E.V. Polujempiricheskie gipotezy teorii turbulentnosti v anizotropnom pogranichnom sloe // Optika atmosf. i okeana. 2005. V. 18, N 10. P. 845–862.
11. Vladimirov V.S. Obobshhennye funkcii v matematicheskoj fizike. M.: Nauka, 1976. 280 p.
12. Nosov V.V., Lukin V.P., Nosov E.V., Botygina N.N., Emaleev O.N., Torgaev A.V. Influence of photodetector response time on operation of monostatic and bistatic airborne meters of turbulence: Part I; Part II // Proc. SPIE. 2006. V. 6522. P. 65220Q; P. 65220R.