Mathematical Methods and Computer Simulation of the Markov Systems and Their Application

Work number - M 1 AWARDED

Presented by V.M.Glushkov Institute of Cybernetics NAS of Ukraine.

Authors: Gupal N.A., KnopovaV.P., OstrovskiyA.V.

New mathematical methods and algorithms based on modern computer technologies for solving some important interdisciplinary theoretical and applied problems arising in economics, financial mathematics, medicine and biology are developed in the present series of works.

The new classes of Markov systems areinvestigated that do not necessarily continuously depend on time, but have a so-called property of loss of memory. For them the series of fundamental results related to finding of basic characteristic and their asymptotic behavior, development of analytical and probability methods allowing to investigate Levy and Levy type processes is got. This, in turn, expanded the range of applied problems, described by such processes.

Fundamental results have been obtained in the development of computer technologies for the analysis of genetic information in genomes and proteins, which have wide application in the study of important problems of bioinformatics. Important aspects of noise immunity of genetic codes, the possibility of optimal noise-immune codes constructing are investigated, a direct connection between point mutations and the emergence of various genetic diseases is found.

The obtained results are new, have priority nature and correspond to the world level of studies, they were repeatedly cited and recognized by this research sphere experts. They were published in prestigious national and foreign scientific journals, presented at international conferences and seminars.

Thus, in the series of works new non-traditional tasks of important classes of Markovian systems are set and the theoretical framework for their study is significantly developed. Some methods for their use in solving of applied problems in biology, medicine, financial and insurance mathematics are proposed.

Common amount of works is 77, including on the work subject: 29 papers (26 – in foreign journals) and 26– the theses of conferences. A common amount of references to the works of the authors is 130 (according to Scopus database), 328 (according to Google Scholar database). h-index of quoting is 7 (according to Scopus database), 10 (according to Google Scholar database).