On the solution of the problem of stochastic stability of the integral manifold by the Lyapunov’s second method
By using the method of Lyapunov functions, we establish sufficient conditions of stability and asymptotic stability in probability for the integral manifold of the Itˆo differential equations in the presence of random perturbations from the class of processes with independent increments. Theorems on...
Збережено в:
| Дата: | 2016 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Російська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2016
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/1818 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | By using the method of Lyapunov functions, we establish sufficient conditions of stability and asymptotic stability in
probability for the integral manifold of the Itˆo differential equations in the presence of random perturbations from the class
of processes with independent increments. Theorems on the stochastic stability of the analytically given integral manifold
of differential equations are proved in the first approximation and under the permanent action of small (in the mean) random
perturbations. |
|---|