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. 
@article{IVM_2014_12_a5,
     author = {Yu. A. Lygin},
     title = {Solution to differential equation with time continuous {Markov} coefficient},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {60--69},
     publisher = {mathdoc},
     number = {12},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2014_12_a5/}
}
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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/