Geodesic
Solution to differential equation with time continuous Markov coefficient
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2014), pp. 60-69.

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We consider first-order differential equations whose stochastic nature is determined by time-continuous Markov's processes. We show that implementation of the Fokker–Plank–Kolmogorov equation leads to a system of advection equation. We formulate a theorem on the characteristics of obtained system of partial differential equations, formulate main derives on necessary conditions for determination of calculation of probability density and adduce an example of the solution.
Keywords: stochastic differential equation, time-continuous Markov process, Fokker–Plank–Kolmogorov equation, probability density, correlation function. 
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Yu. A. Lygin. Solution to differential equation with time continuous Markov coefficient. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2014), pp. 60-69. http://geodesic.mathdoc.fr/item/IVM_2014_12_a5/

[1] Uleman J. S., Rim S. S., Saribay S. A., Kressel L. M., “Controversies, questions, and prospects for spontaneous social inferences”, Social and Personality Psychology Compass, 6:9 (2012), 657–673 | DOI

[2] Scott A. B., “Hayek on spontaneous order and constitutional design”, The Independent Review, 15:1 (2010), 19–34

[3] Miloslav I., “Obyknovennye differentsialnye i raznostnye uravneniya so sluchainymi koeffitsientami i sluchainoi pravoi chastyu”, Czechoslovak Math. J., 12:3 (1962), 457–474

[4] Pugachev V. S., Sinitsyn I. N., Stokhasticheskie differentsialnye sistemy. Analiz i filtratsiya, Nauka, M., 1990 | MR | Zbl

[5] Tikhonov V. I., Kulman N. K., Nelineinaya filtratsiya i kvazikogerentnyi priem signalov, Sov. radio, M., 1975

[6] Kurant R., Uravneniya s chastnymi proizvodnymi, Mir, M., 1964 | MR

[7] Lygin Yu. A., “Matematicheskaya model shuma, voznikayuschego pri prokhozhdenii tyagovogo toka cherez kontakt koleso–rels”, Materialy Vserossiiskoi nauchno-prakticheskoi konferentsii “Transport-2013” (Rostov-na-Donu, 24–26 aprelya 2013), Izd-vo Rost. gos. un-ta putei soobscheniya, Rostov n/D, 2013, 48–50

[8] Lygin Yu. A., “Model dinamiki osnovnykh fondov s uchetom nedostatochnoi kompetentsii obsluzhivayuschego personala”, Materialy nauchno-prakticheskoi konferentsii “Informatsionnye tekhnologii v ekonomicheskikh issledovaniyakh” (Rostov-na-Donu, 30 oktyabrya 2012), Izd-vo Donsk. gos. tekhn. un-ta, Rostov n/D, 2013, 105–111

[9] Guseva L. L., Orudzheva A. A., Taran V. N., “Matematicheskoe modelirovanie obrazovatelnoemkosti trudovogo potentsiala v sisteme vysshego obrazovaniya”, Vestnik Rostovsk. gos. un-ta putei soobscheniya, 2012, no. 1, 101–107