A dynamical system with random parameters as a mathematical model of real phenomena
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In many cases, it is difcult to nd 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 coefcients 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.
KeywordsMarkov and semi-Markov chain, random transformation of solutions, L2-stability, jumps of solutions, moment equations
Document typePeer reviewed
Document versionFinal PDF
SourceSymmetry. 2019, vol. 11, issue 11, p. 1-14.