Geodesic
Statistical characteristics of solutions of the system of the stochastic transfer model
Matematičeskoe modelirovanie, Tome 32 (2020) no. 5, pp. 21-43.

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The paper proposes a new stochastic transport model formalized in the framework of differential equations with random parameters. Explicit formulas for the mathematical expectation and the second-moment function for solving the corresponding equations are given. The estimation of the influence of random factors on the system, in the case of replacing the random coefficient of the equation by its mathematical expectation, is determined. An example with Gaussian distribution of random coefficients is also presented and discusser. The paper shows that the proposed model is applicable to the description of heat and moisture transfer processes in the surface layer of the atmosphere.
Keywords: stochastic model, random process, characteristic functional, mathematical expectation, dispersion function, influence of random factors. 
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V. G. Zadorozhniy; M. E. Semenov; N. I. Sel'vesyuk; I. I. Ulshin; V. S. Nozhkin. Statistical characteristics of solutions of the system of the stochastic transfer model. Matematičeskoe modelirovanie, Tome 32 (2020) no. 5, pp. 21-43. http://geodesic.mathdoc.fr/item/MM_2020_32_5_a1/

[1] M. L. Salby, Fundamentals of Atmospheric Physics, Academic Press, NY, 1996, 376 pp.

[2] M. A. Tolstykh, “Globalnye modeli atmosfery: sovremennoe sostoianie i perspektivy razvitiia”, Trudy GNITS Rossiiskoi Federatsii, 2016, no. 359, 5–32

[3] Gidromettsentr Rossii (Data obrashcheniia: 13.05.2019)

[4] E. N. Lorenz, “Deterministic nonperiodic flow”, Journal of the atmospheric sciences, 20 (1963), 130–141 | 2.0.CO;2 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[5] A. N. Bagrov, “Operativnaia chislennaia skhema prognoza konvektivnykh iavlenii (kuchevoobraznoi oblachnosti, livnei, groz i shkvalov) i oblozhnykh osadkov”, Trudy GMTS, 1972, no. 91, 29–38

[6] B. D. Uspenskii, “Kolichestvennyi prognoz oblozhnykh i livnevych osadkov”, Meteorologiia i gidrologiia, 1970, no. 1, 11–18

[7] V. G. Zadorozhniy, “Stabilization of Linear Systems by a Multiplicative Random Noise”, Differential Equations, 54:6 (2018), 728–747 | DOI | DOI | MR | Zbl

[8] V. G. Zadorozhnii, Metody variatsionnogo analiza, RKHD, M.–Izhevsk, 2006, 316 pp.

[9] V. G. Zadorozhniy, “Linear chaotic resonance in vortex motion”, Comp. Math. Math. Phys., 53:4 (2013), 486–502 | DOI | MR | Zbl

[10] P. G. Friik, Turbulentnost: Podkhody i modeli, IKI, M.–Igevsk, 2003, 291 pp.

[11] B. Oksendal, Stochastic differential equations, Springer, Berlin, 2003, 379 pp. | MR | Zbl

[12] A. N. Kolmogorov, S. V. Fomin, Elementy teorii funktsii i funktsionalnogo analiza, 6-e izd., ispravl., Nauka, M., 1989, 624 pp. | MR

[13] G. E. Shilov, Matematicheskii analiz. Vtoroi spetsialnyi kurs, Nauka, M., 1965, 328 pp.

[14] V. S. Nozhkin et al, “Stochastic model of moisture motion in atmosphere”, Journal of Physics: Conference Series, 1096 (2018), 012167 | DOI

[15] V. S. Vladimirov, Generalized functions in mathematical physics, Mir Publishers, 1979, 390 pp.