Stochastic invariance for hybrid stochastic differential equation with non-Lipschitz coefficients
In this paper, by using of the martingale property and positive maximum principle, we investigate the stochastic invariance for a class of hybrid stochastic differential equations (HSDEs) and provide necessary and sufficient conditions for the invariance of closed sets of $\mathbb{R}^d$ with non-Lip...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2020-05-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/10.3934/math.2020234/fulltext.html |
| _version_ | 1819016440884232192 |
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| author | Chunhong Li Sanxing Liu |
| author_facet | Chunhong Li Sanxing Liu |
| author_sort | Chunhong Li |
| collection | DOAJ |
| description | In this paper, by using of the martingale property and positive maximum principle, we investigate the stochastic invariance for a class of hybrid stochastic differential equations (HSDEs) and provide necessary and sufficient conditions for the invariance of closed sets of $\mathbb{R}^d$ with non-Lipschitz coefficients. Moreover, an example of the most probable phase portrait is given to illustrate the effectiveness of the main results. |
| first_indexed | 2024-12-21T02:47:40Z |
| format | Article |
| id | doaj.art-028da6cd5c26425b87ff50ff037c40ea |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-21T02:47:40Z |
| publishDate | 2020-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-028da6cd5c26425b87ff50ff037c40ea2022-12-21T19:18:31ZengAIMS PressAIMS Mathematics2473-69882020-05-01543612363310.3934/math.2020234Stochastic invariance for hybrid stochastic differential equation with non-Lipschitz coefficientsChunhong Li0Sanxing Liu11 School of Mathematics and Information Sciences, Guangzhou University, Guangzhou, Guangdong 510006, PR China 2 School of civil Engineering, Jiaying University, Meizhou, Guangdong 514015, PR China1 School of Mathematics and Information Sciences, Guangzhou University, Guangzhou, Guangdong 510006, PR China 2 School of civil Engineering, Jiaying University, Meizhou, Guangdong 514015, PR ChinaIn this paper, by using of the martingale property and positive maximum principle, we investigate the stochastic invariance for a class of hybrid stochastic differential equations (HSDEs) and provide necessary and sufficient conditions for the invariance of closed sets of $\mathbb{R}^d$ with non-Lipschitz coefficients. Moreover, an example of the most probable phase portrait is given to illustrate the effectiveness of the main results.https://www.aimspress.com/article/10.3934/math.2020234/fulltext.htmllinear growth conditionmartingale problemhybrid stochastic differential equationsstochastic invariance |
| spellingShingle | Chunhong Li Sanxing Liu Stochastic invariance for hybrid stochastic differential equation with non-Lipschitz coefficients AIMS Mathematics linear growth condition martingale problem hybrid stochastic differential equations stochastic invariance |
| title | Stochastic invariance for hybrid stochastic differential equation with non-Lipschitz coefficients |
| title_full | Stochastic invariance for hybrid stochastic differential equation with non-Lipschitz coefficients |
| title_fullStr | Stochastic invariance for hybrid stochastic differential equation with non-Lipschitz coefficients |
| title_full_unstemmed | Stochastic invariance for hybrid stochastic differential equation with non-Lipschitz coefficients |
| title_short | Stochastic invariance for hybrid stochastic differential equation with non-Lipschitz coefficients |
| title_sort | stochastic invariance for hybrid stochastic differential equation with non lipschitz coefficients |
| topic | linear growth condition martingale problem hybrid stochastic differential equations stochastic invariance |
| url | https://www.aimspress.com/article/10.3934/math.2020234/fulltext.html |
| work_keys_str_mv | AT chunhongli stochasticinvarianceforhybridstochasticdifferentialequationwithnonlipschitzcoefficients AT sanxingliu stochasticinvarianceforhybridstochasticdifferentialequationwithnonlipschitzcoefficients |