This article is cited in 2 papers

Solution to differential equation with time continuous Markov coefficient

Yu. A. Lygin

Rostov State Transport University, 2 Rostovskogo Strelkovogo Polka Narodnogo Opolchenija Sq., Rostov-on-Don, 344038 Russia

Abstract: 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.

UDC: 517.926

Received: 17.06.2013

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2014, 58:12, 51–58

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