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DIBLÍK, J. DZHALLADOVA, I. RŮŽIČKOVÁ, M.
Original Title
A dynamical system with random parameters as a mathematical model of real phenomena
Type
journal article in Web of Science
Language
English
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.
Keywords
Markov and semi-Markov chain; random transformation of solutions; L2-stability; jumps of solutions; moment equations
Authors
DIBLÍK, J.; DZHALLADOVA, I.; RŮŽIČKOVÁ, M.
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
State
Swiss Confederation
Pages from
1
Pages to
14
Pages count
URL
https://www.mdpi.com/2073-8994/11/11/1338
Full text in the Digital Library
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" }