Detail publikace

A dynamical system with random parameters as a mathematical model of real phenomena

DIBLÍK, J. DZHALLADOVA, I. RŮŽIČKOVÁ, M.

Originální název

A dynamical system with random parameters as a mathematical model of real phenomena

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

Originální abstrakt

In many cases, it is difficult to find a solution to a system of difference equations with random structure in a closed form. Thus, a random process, which is the solution to such a system, can be described in another way, for example, by its moments. In this paper, we consider systems of linear difference equations whose coefficients depend on a random Markov or semi-Markov chain with jumps. The moment equations are derived for such a system when the random structure is determined by a Markov chain with jumps. As an example, three processes: Threats to security in cyberspace, radiocarbon dating, and stability of the foreign currency exchange market are modelled by systems of difference equations with random parameters that depend on a semi-Markov or Markov process. The moment equations are used to obtain the conditions under which the processes are stable.

Klíčová slova

Markov and semi-Markov chain; random transformation of solutions; L2-stability; jumps of solutions; moment equations

Autoři

DIBLÍK, J.; DZHALLADOVA, I.; RŮŽIČKOVÁ, M.

Vydáno

30. 10. 2019

Nakladatel

MDPI

Místo

MDPI AG, ST ALBAN-ANLAGE 66, CH-4052 BASEL, SWITZERLAND

ISSN

2073-8994

Periodikum

Symmetry

Ročník

11

Číslo

11

Stát

Švýcarská konfederace

Strany od

1

Strany do

14

Strany počet

14

URL

https://www.mdpi.com/2073-8994/11/11/1338

Plný text v Digitální knihovně

http://hdl.handle.net/11012/184671

BibTex

@article{BUT159586,
  author="Josef {Diblík} and Irada {Dzhalladova} and Miroslava {Růžičková}",
  title="A dynamical system with random parameters as a mathematical model of real phenomena",
  journal="Symmetry",
  year="2019",
  volume="11",
  number="11",
  pages="1--14",
  doi="10.3390/sym11111338",
  issn="2073-8994",
  url="https://www.mdpi.com/2073-8994/11/11/1338"
}