Publication detail

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

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

Original Title

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

English Title

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

Type

journal article in Web of Science

Language

en

Original Abstract

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.

English abstract

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.

Keywords

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

Released

30.10.2019

Publisher

MDPI

Location

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

ISBN

2073-8994

Periodical

Symmetry

Year of study

11

Number

11

State

CH

Pages from

1

Pages to

14

Pages count

14

URL

Full text in the Digital Library

Documents

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",
  annote="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.",
  address="MDPI",
  chapter="159586",
  doi="10.3390/sym11111338",
  howpublished="online",
  institution="MDPI",
  number="11",
  volume="11",
  year="2019",
  month="october",
  pages="1--14",
  publisher="MDPI",
  type="journal article in Web of Science"
}