Backward Doubly Stochastic Differential Equations with Markov Chains and a Comparison Theorem
In this paper we study the existence and uniqueness of solutions for one kind of backward doubly stochastic differential equations (BDSDEs) with Markov chains. By generalizing the Itô’s formula, we study such problem under the Lipschitz condition. Moreover, thanks to the Yosida approximation, we sol...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-11-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/12/1953 |
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doaj-2d831adb2c5c407f84afff5d6298ae742020-11-27T08:08:55ZengMDPI AGSymmetry2073-89942020-11-01121953195310.3390/sym12121953Backward Doubly Stochastic Differential Equations with Markov Chains and a Comparison TheoremNing Ma0Zhen Wu1School of Mathematics, Shandong University, Jinan 250100, ChinaSchool of Mathematics, Shandong University, Jinan 250100, ChinaIn this paper we study the existence and uniqueness of solutions for one kind of backward doubly stochastic differential equations (BDSDEs) with Markov chains. By generalizing the Itô’s formula, we study such problem under the Lipschitz condition. Moreover, thanks to the Yosida approximation, we solve such problem under monotone condition. Finally, we give the comparison theorems for such equations under the above two conditions respectively.https://www.mdpi.com/2073-8994/12/12/1953backward doubly stochastic differential equationsMarkov chainscomparison theorem |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Ning Ma Zhen Wu |
| spellingShingle |
Ning Ma Zhen Wu Backward Doubly Stochastic Differential Equations with Markov Chains and a Comparison Theorem Symmetry backward doubly stochastic differential equations Markov chains comparison theorem |
| author_facet |
Ning Ma Zhen Wu |
| author_sort |
Ning Ma |
| title |
Backward Doubly Stochastic Differential Equations with Markov Chains and a Comparison Theorem |
| title_short |
Backward Doubly Stochastic Differential Equations with Markov Chains and a Comparison Theorem |
| title_full |
Backward Doubly Stochastic Differential Equations with Markov Chains and a Comparison Theorem |
| title_fullStr |
Backward Doubly Stochastic Differential Equations with Markov Chains and a Comparison Theorem |
| title_full_unstemmed |
Backward Doubly Stochastic Differential Equations with Markov Chains and a Comparison Theorem |
| title_sort |
backward doubly stochastic differential equations with markov chains and a comparison theorem |
| publisher |
MDPI AG |
| series |
Symmetry |
| issn |
2073-8994 |
| publishDate |
2020-11-01 |
| description |
In this paper we study the existence and uniqueness of solutions for one kind of backward doubly stochastic differential equations (BDSDEs) with Markov chains. By generalizing the Itô’s formula, we study such problem under the Lipschitz condition. Moreover, thanks to the Yosida approximation, we solve such problem under monotone condition. Finally, we give the comparison theorems for such equations under the above two conditions respectively. |
| topic |
backward doubly stochastic differential equations Markov chains comparison theorem |
| url |
https://www.mdpi.com/2073-8994/12/12/1953 |
| work_keys_str_mv |
AT ningma backwarddoublystochasticdifferentialequationswithmarkovchainsandacomparisontheorem AT zhenwu backwarddoublystochasticdifferentialequationswithmarkovchainsandacomparisontheorem |
| _version_ |
1724413677483851776 |