Applied Lyapunov Stability for Some Nonlinear Stochastic Differential Equations
In this paper, we applied and explain the stability to some linear and non-linear stochastic differential equations by using the Lyapunov direct second method, after finding the stochastic differential equation which obtained by applying the (Ito-integrated formula) and the quadratic Lyapunov fun...
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| Format: | Article |
| Language: | English |
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Tikrit University
2023-10-01
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| Series: | Tikrit Journal of Pure Science |
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| Online Access: | https://tjpsj.org/index.php/tjps/article/view/1586 |
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| author | Nibal Sabah Abdurahman Abdulghafoor Jasim Salim |
| author_facet | Nibal Sabah Abdurahman Abdulghafoor Jasim Salim |
| author_sort | Nibal Sabah Abdurahman |
| collection | DOAJ |
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In this paper, we applied and explain the stability to some linear and non-linear stochastic differential equations by using the Lyapunov direct second method, after finding the stochastic differential equation which obtained by applying the (Ito-integrated formula) and the quadratic Lyapunov function be taken, we use the Lyapunov theorems to find and explain if the trivial (zero) solution are stochastically stabile (p-stable, mean square stable and stochastically asymptotically stable in the large ), then we explain the methods by some examples.
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| format | Article |
| id | doaj-art-6d87a5a78cf343189a46fb43bfe99876 |
| institution | OA Journals |
| issn | 1813-1662 2415-1726 |
| language | English |
| publishDate | 2023-10-01 |
| publisher | Tikrit University |
| record_format | Article |
| series | Tikrit Journal of Pure Science |
| spelling | doaj-art-6d87a5a78cf343189a46fb43bfe998762025-08-20T02:36:22ZengTikrit UniversityTikrit Journal of Pure Science1813-16622415-17262023-10-0128510.25130/tjps.v28i5.1586Applied Lyapunov Stability for Some Nonlinear Stochastic Differential EquationsNibal Sabah Abdurahman 0Abdulghafoor Jasim Salim1Department of Mathematics, College of Education for pure Science, The University of Mosul. Mosul – IraqDepartment of Mathematics, College of Computer Science and Mathematics, The University of Mosul. Mosul – Iraq In this paper, we applied and explain the stability to some linear and non-linear stochastic differential equations by using the Lyapunov direct second method, after finding the stochastic differential equation which obtained by applying the (Ito-integrated formula) and the quadratic Lyapunov function be taken, we use the Lyapunov theorems to find and explain if the trivial (zero) solution are stochastically stabile (p-stable, mean square stable and stochastically asymptotically stable in the large ), then we explain the methods by some examples. https://tjpsj.org/index.php/tjps/article/view/1586stabilitystochastic(random) differential equationthe Lyapunov function. |
| spellingShingle | Nibal Sabah Abdurahman Abdulghafoor Jasim Salim Applied Lyapunov Stability for Some Nonlinear Stochastic Differential Equations Tikrit Journal of Pure Science stability stochastic(random) differential equation the Lyapunov function. |
| title | Applied Lyapunov Stability for Some Nonlinear Stochastic Differential Equations |
| title_full | Applied Lyapunov Stability for Some Nonlinear Stochastic Differential Equations |
| title_fullStr | Applied Lyapunov Stability for Some Nonlinear Stochastic Differential Equations |
| title_full_unstemmed | Applied Lyapunov Stability for Some Nonlinear Stochastic Differential Equations |
| title_short | Applied Lyapunov Stability for Some Nonlinear Stochastic Differential Equations |
| title_sort | applied lyapunov stability for some nonlinear stochastic differential equations |
| topic | stability stochastic(random) differential equation the Lyapunov function. |
| url | https://tjpsj.org/index.php/tjps/article/view/1586 |
| work_keys_str_mv | AT nibalsabahabdurahman appliedlyapunovstabilityforsomenonlinearstochasticdifferentialequations AT abdulghafoorjasimsalim appliedlyapunovstabilityforsomenonlinearstochasticdifferentialequations |