Detail publikace

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

Originální název

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

Anglický název

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

Jazyk

en

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.

Anglický 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.

Plný text v Digitální knihovně

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"
}