Б а с р е д а к т о р ы ф.-м.ғ.д., проф., ҚР ҰҒА академигі Ғ.М. Мұтанов Р е д а к ц и я а л қ а с ы: Жұмаділдаев А.С. проф., академик (Қазақстан) Кальменов Т.Ш. проф., академик (Қазақстан) Жантаев Ж.Ш. проф., корр.-мүшесі (Қазақстан) Өмірбаев У.У. проф. корр.-мүшесі (Қазақстан) Жүсіпов М.А. проф. (Қазақстан) Жұмабаев Д.С. проф. (Қазақстан) Асанова А.Т. проф. (Қазақстан) Бошкаев К.А. PhD докторы (Қазақстан) Сұраған Д. корр.-мүшесі (Қазақстан) Quevedo Hernando проф. (Мексика), Джунушалиев В.Д. проф. (Қырғыстан) Вишневский И.Н. проф., академик (Украина) Ковалев А.М. проф., академик (Украина) Михалевич А.А. проф., академик (Белорус) Пашаев А. проф., академик (Əзірбайжан) Такибаев Н.Ж. проф., академик (Қазақстан), бас ред. орынбасары Тигиняну И. проф., академик (Молдова) «ҚР ҰҒА Хабарлары. Физика-математикалық сериясы».
One of the inverse problems of dynamics in the presence of random perturbations is considered. This is the problem of the simultaneous construction of a set of first-order Ito stochastic differential equations with a given integral manifold, and a set of comparison functions. The given manifold is stable in probability with respect to these comparison functions.
A problem with parameter for an
integro-differential equation is approximated by a
problem with parameter for a loaded differential equation.
The well-posedness of a problem with parameter for the
integro-differential equation is established in the terms of the well-posedness of a problem with parameter for the loaded differential equation. A mutual relationship between the qualitative properties of original
and approximate problems is obtained, and the estimates for
differences between their solutions are set.
A new general solution to the
loaded differential equation with parameter is presented, and its properties are described. The problem with parameter for the loaded differential equation
is reduced to a system of linear algebraic equations
with respect to the arbitrary vectors of a general solution
introduced. The system’s coefficients and right-hand sides are computed
by solving the Cauchy problems for ordinary differential
equations.
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