Reflected generalized BDSDEs driven by non-homogeneous Lévy processes and obstacle problems for stochastic integro-PDEs with nonlinear Neumann boundary conditions
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910030767325184 |
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| author | Elmansouri, Badr Elhachemy, Mohammed Marzougue, Mohamed Jamali, Mohamed El |
| author_facet | Elmansouri, Badr Elhachemy, Mohammed Marzougue, Mohamed Jamali, Mohamed El |
| contents | We consider reflected generalized backward doubly stochastic differential equations driven by a non-homogeneous Lévy process. Under stochastic conditions on the coefficients, we prove the existence and uniqueness of a solution. Furthermore, we apply these results to obtain a probabilistic representation for the viscosity solutions of an obstacle problem governed by stochastic integro-partial differential equations with a nonlinear Neumann boundary condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_25912 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reflected generalized BDSDEs driven by non-homogeneous Lévy processes and obstacle problems for stochastic integro-PDEs with nonlinear Neumann boundary conditions Elmansouri, Badr Elhachemy, Mohammed Marzougue, Mohamed Jamali, Mohamed El Probability 60H05, 60H15, 60H20, 60H30 We consider reflected generalized backward doubly stochastic differential equations driven by a non-homogeneous Lévy process. Under stochastic conditions on the coefficients, we prove the existence and uniqueness of a solution. Furthermore, we apply these results to obtain a probabilistic representation for the viscosity solutions of an obstacle problem governed by stochastic integro-partial differential equations with a nonlinear Neumann boundary condition. |
| title | Reflected generalized BDSDEs driven by non-homogeneous Lévy processes and obstacle problems for stochastic integro-PDEs with nonlinear Neumann boundary conditions |
| topic | Probability 60H05, 60H15, 60H20, 60H30 |
| url | https://arxiv.org/abs/2509.25912 |