# American Institute of Mathematical Sciences

January  2018, 23(1): 473-485. doi: 10.3934/dcdsb.2018032

## Solution to a stochastic pursuit model using moment equations

 1 University of Białystok, Faculty of Mathematics and Informatics, K. Ciołkowskiego 1M, 15-245 Białystok, Poland 2 Kiev National Economics V. Hetman University Faculty of Information System and Technology, Kyiv 03068, Peremogy 54/1, Ukraine 3 Palacký University Olomouc, Faculty of Education, Žižkovo nám. 5, Olomouc, Czech Republic 4 Brno University of Technology, Faculty of Civil Engineering, Department of Mathematics and Descriptive Geometry, Veveří 331/95,602 00 Brno, Czech Republic

* Corresponding author: Miroslava Růžičková

Received  September 2016 Published  January 2018

The paper investigates the navigation problem of following a moving target, using a mathematical model described by a system of differential equations with random parameters. The differential equations, which employ controls for following the target, are solved by a new approach using moment equations. Simulations are presented to test effectiveness of the approach.

Citation: Miroslava Růžičková, Irada Dzhalladova, Jitka Laitochová, Josef Diblík. Solution to a stochastic pursuit model using moment equations. Discrete & Continuous Dynamical Systems - B, 2018, 23 (1) : 473-485. doi: 10.3934/dcdsb.2018032
##### References:

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##### References:
Distribution of forces acting on the missile
The mean value of the process s(t) with parameters λ and p: λ = 0.01; p = 0.1, 0.2, ..., 1; s(0) = 0, 4, 8, ..., 200
The mean value of the process s(t) with parameters λ and p: λ = 0.01, 0.02, ..., 0.2; p = 0.1, 0.2, ..., 1; s(0) = 0, 4, 8, ..., 200
The mean value of the process $s(t)$ with parameters $\lambda$ and $p$: $\lambda=0.01, 0.011, 0.012, \ldots, 0.21$; $p=0, 0.01, \ldots, 1$; $s(0)=0$
The mean value of the process $s(t)$ with parameters $\lambda$ and $p$: $\lambda=0.01, 0.011, 0.012, \ldots, 0.21$; $p=0, 0.01, \ldots, 1$; $s(0)=0, 20, \ldots, 100$
The mean value $E_{1}^{(1)}\{s( t )\}$ of the stochastic process as the solution to (12) and the mean value of two simulations of the stochastic process
The mean value $E_{1}^{(1)}\{s( t )\}$ of the stochastic process as the solution to(12) and the mean value of one hundred simulations of the stochastic process
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