# On construction of the comparison function of program motion in probable statement

 dc.contributor.author Vassilina, G.K. dc.contributor.author Tleubergenov, M.I. dc.date.accessioned 2019-10-30T09:02:26Z dc.date.available 2019-10-30T09:02:26Z dc.date.issued 2019-09-30 dc.identifier.citation Vassilina, G.K. On construction of the comparison function of program motion in probable statement / G.K. Vassilina, M.I. Tleubergenov // Қарағанды универисетінің хабаршысы. Математика сериясы. = Вестник Карагандинского университета. Серия Математика. = Bulletin of the Karaganda University. Mathematics series. – 2019. - № 3. – P. 60-67. ru_RU dc.identifier.issn 2518-7929 dc.identifier.issn 2663-5011 dc.identifier.uri http://rep.ksu.kz//handle/data/8531 dc.description.abstract In the class of ordinary differential equations the following modification of the inverse problem of differential systems was previously considered: to construct both a set of systems of differential equations and a set of comparison functions for the given program motion. In this article, the modification of the inverse problem is considered in Stochastic case. In this problem it is assumed that random perturbations are from the class of processes with independent increments. By the given program of motion, two sets are constructed: the set of first-order Itoˆ stochastic differential equations and the set of comparison functions. It is proved that there is a stability in probability of the given program motion with respect to the constructed comparison functions. To solve the problem Lyapunov functions method is used. Using Lyapunov’s second method makes it is possible to weaken the conditions imposed on the components of the constructed comparison functions, in contrast to the application of the Lyapunov characteristic numbers method for solving the inverse problem in the class of ordinary differential equations. The following cases are considered: 1) comparison functions obviously not depending on time; 2) the set of comparison vector functions depends on y and t; 3) the set of comparison vector functions has the form Q(λ, t, where λ(y, t) describes an analytically given program motion; 4) the set of comparison vector functions has the form C(t)λ. ru_RU dc.language.iso en ru_RU dc.publisher Ye.A.Buketov Karaganda State University Publishing house ru_RU dc.relation.ispartofseries Қарағанды универисетінің хабаршысы. Математика сериясы. = Вестник Карагандинского университета. Серия Математика. = Bulletin of the Karaganda University. Mathematics series.;№ 3(95)/2019 dc.subject stochastic differential equations ru_RU dc.subject inverse problems ru_RU dc.subject stability in probability ru_RU dc.subject comparison function ru_RU dc.subject program motion ru_RU dc.subject random process ru_RU dc.title On construction of the comparison function of program motion in probable statement ru_RU dc.title.alternative Ықтималды жағдайдағы бағдарламалық қозғалыстың салыстыру фунциясының қүрылуы туралы ru_RU dc.title.alternative О построении функции сравнения программного движения в вероятностной постановке ru_RU dc.type Article ru_RU
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