Solution to a stochastic pursuit model using moment equations

Miroslava Růžičková; Irada Dzhalladova; Jitka Laitochová; Josef Diblík

doi:10.3934/dcdsb.2018032

Article Contents

2018, Volume 23, Issue 1: 473-485. Doi: 10.3934/dcdsb.2018032

This issue Previous Article Does assortative mating lead to a polymorphic population? A toy model justification Next Article On homoclinic solutions for a second order difference equation with p-Laplacian

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
^* Corresponding author: Miroslava Růžičková

Received: September 2016

Published: November 2017

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Abstract

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.

Keywords:

Stochastic pursuit model,
differential equations with random parameters,
Markov process,
moment equations,
simulation of stochastic process.

Mathematics Subject Classification: Primary: 34F05; Secondary: 60J28.

Citation:

Full Text(HTML)

Figure 1. Distribution of forces acting on the missile

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Figure 2. 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

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Figure 3. 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

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Figure 4. The mean value of the process $s(t)$ with parameters $\lambda$ and $p$: $\lambda=0.01, 0.011, 0.012, \ldots, 0.21$; $p=0, 0.01, \ldots, 1$; $s(0)=0$

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Figure 5. The mean value of the process $s(t)$ with parameters $\lambda$ and $p$: $\lambda=0.01, 0.011, 0.012, \ldots, 0.21$; $p=0, 0.01, \ldots, 1$; $s(0)=0, 20, \ldots, 100$

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Figure 6. 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

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Figure 7. 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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