McKean-Vlasov forward-backward doubly stochastic differential equations and applications to stochastic control
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910523654668288 |
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| author | Al-Hussein, AbdulRahman Ninouh, Abdelhakim Gherbal, Boulakhras |
| author_facet | Al-Hussein, AbdulRahman Ninouh, Abdelhakim Gherbal, Boulakhras |
| contents | This paper investigates first the existence and uniqueness of solutions for McKean-Vlasov forward-backward doubly stochastic differential equations (MV-FBDSDEs) in infinite-dimensional real separable Hilbert spaces. These equations combine the features of forward-backward doubly stochastic differential equations with the mean-field approach, allowing the coefficients to depend on the solution distribution. We establish the existence and uniqueness of solutions for MV-FBDSDEs using the method of continuation and provide an example and a counterexample to illustrate our findings. Moreover, we extend the practical applicability of our results by employing them within the context of the stochastic maximum principle for a control problem governed by MV-FBDSDEs. This study contributes to the field of stochastic control problems and presents the first analysis of MV-FBDSDEs in infinite-dimensional spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07881 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | McKean-Vlasov forward-backward doubly stochastic differential equations and applications to stochastic control Al-Hussein, AbdulRahman Ninouh, Abdelhakim Gherbal, Boulakhras Probability Optimization and Control 60H10, 93E20 This paper investigates first the existence and uniqueness of solutions for McKean-Vlasov forward-backward doubly stochastic differential equations (MV-FBDSDEs) in infinite-dimensional real separable Hilbert spaces. These equations combine the features of forward-backward doubly stochastic differential equations with the mean-field approach, allowing the coefficients to depend on the solution distribution. We establish the existence and uniqueness of solutions for MV-FBDSDEs using the method of continuation and provide an example and a counterexample to illustrate our findings. Moreover, we extend the practical applicability of our results by employing them within the context of the stochastic maximum principle for a control problem governed by MV-FBDSDEs. This study contributes to the field of stochastic control problems and presents the first analysis of MV-FBDSDEs in infinite-dimensional spaces. |
| title | McKean-Vlasov forward-backward doubly stochastic differential equations and applications to stochastic control |
| topic | Probability Optimization and Control 60H10, 93E20 |
| url | https://arxiv.org/abs/2406.07881 |