Abstract
A mathematical model of Lanchester’s combat operations is studied in the form of a system of differential equations, whose coefficients are random processes. It is assumed that the random coefficients are given by the characteristic functional. The first and second moment functions of system solutions are found. The problem is reduced to a deterministic system of differential equations with ordinary and variational derivatives. Gaussian and uniformly distributed random coefficients are considered.
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References
Lanchester, F.: Aircraft in Warfare: The Dawn of the Fourth Arm, pp. 1916–243. Constable and Co, London
Osipov, M.: Vliyaniye chislennosti srazhayuschihsya storon na ih poteri. Voennyi sbornik, 1915, 6, p. 59–74, 7, p. 25–30, 8, p/31–40, 9, p. 25–37 (in rus.)
Gordin, V.A.: Differentsialnye i raznostnye uravneniya. kakie yravleniya oni opisyvayut i kak ih reshat. Natsionalnye issledovaniya un-t “vyschaya shkola ekonomiki”, M.: Izd. Dom Vyschey shkoly ekonomiki, 2016 (in rus.)
Novikov, D.A.: Ierharicheskie modeli voennyh deystviy. UBS 37, 25–62 (2012). Autom. Remote Control 74(10), 1733–1752 (2013) (in rus.)
Ventzel, E.S.: Vvedenie v issledovanie operatsiy, M.: Sov. radio (1964) (in rus.)
Vasilyev, G.A., Kazakov, V.G., Tarakanov, A.F.: Teoretiko-igrovoe modelirovanie protivostoyaniya storon na osnove refleksivnogo upravleniya. Problemy upravleniya 5, 49–55 (2018) (in rus.)
Chumov, V.V.: Ierarhiya modeley boevyh deystviy i pogranichnyh konfliktov. UBS 70, 122–130 (2019) (in rus.)
Chumov, V.V.: Ierarhicheskie i matrichnye modeli pogranichnoy bezopasnosti. Matematicheskoe modelirovanie 26(3), 137–148 (2014) (in rus.)
Mackay, N.J.: When Lanchester met Richardson, the outcome was Stalemate :a parable for mathematical models of insurgency / N.J. Mackay. J. Oper. Res. Soc. 66(2), 191–201 (2015)
Ganicheva, A.V.: Modifitsirovannaya model Lanchestera boevyh deysyviy. Matematicheskoe modelirivanie 4(58), 72–81 (2019) (in rus.)
Kress, M.: Lanchester mode for three-way combat/ M. Kress, J.P. Caulkins, G. Feichtinger, D. Grass, A. Seide. Eur. J. Oper. Res. 264(1), 46–54 (2018)
Chuev, V.Yu., Dubogray, I.V.: Veroyatnostnaya model boya mnogochislennyh gruppirovok pri lineynyh zavisimostyah effektivyh skorostrelnostey boevyh edits storon ot vremeni boya. Matematicheskoe modelirovanie i chislennye metody 2, 122–132 (2018) (in rus.)
Chuev, V.Yu.: Veroyatnostnaya model boya mnogochislennyh gruppirovok, Vestnik MGTU im. N.E. Baumana ser. Estestvennye nauki (2011), Spets. vyp. “Matematicheskoe modelirovanie”, 223–232 (in rus.)
Fursikov, A.V.: Momentnaya teoriya glya urevneniy Novie-Stoksa so sluchaynoy pravoy chastyu. Izv. RAN. Ser. matem. 56, 1273–1315 1992 (in rus.)
Fursikov, A.V.: Razreshimost zepochki uravneniy dlya prostranstvenno-vremennyh momentov. Mat. sb. 125(167), 3(11), 548–553 (1984) (in rus.)
Adomian, D.: Stohasticheskie sistemy. M.: Mir (1987) (in rus.)
Zadorozhniy, V.G.: Metody variatsionnogo analiza. M.-Izhevsk: RHD (2006) (in rus.)
Zadorozhniy, V.G., Konovalova, M.A.: Multiplikativno vozmuschennoe sluchaynym shumom differentsialnoe uravnenie v banahovom prostranstve, Sovremennaya matematika. Fundamentalnye napravleniya 63(4), 1–16 (2017) (in rus.)
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Zadorozhniy, V.G. (2021). Lanchester Model with the Random Coefficients. In: Karapetyants, A.N., Pavlov, I.V., Shiryaev, A.N. (eds) Operator Theory and Harmonic Analysis. OTHA 2020. Springer Proceedings in Mathematics & Statistics, vol 358. Springer, Cham. https://doi.org/10.1007/978-3-030-76829-4_22
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DOI: https://doi.org/10.1007/978-3-030-76829-4_22
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