$\mathbb{L}^p$-solution of generalized BSDEs in a general filtration with stochastic monotone coefficients
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910801445519360 |
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| author | Elmansouri, Badr Otmani, Mohamed El |
| author_facet | Elmansouri, Badr Otmani, Mohamed El |
| contents | We study multidimensional generalized backward stochastic differential equations (GBSDEs) within a general filtration that supports a Brownian motion under weak assumptions on the associated data. We establish the existence and uniqueness of solutions in $\mathbb{L}^p$ for $p \in (1,2]$. Our results apply to generators that are stochastic monotone in the $y$-variable, stochastic Lipschitz in the $z$-variable, and satisfy a general stochastic linear growth condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15600 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $\mathbb{L}^p$-solution of generalized BSDEs in a general filtration with stochastic monotone coefficients Elmansouri, Badr Otmani, Mohamed El Probability 60H05, 60H10, 34F05, 35R60, 60H30 We study multidimensional generalized backward stochastic differential equations (GBSDEs) within a general filtration that supports a Brownian motion under weak assumptions on the associated data. We establish the existence and uniqueness of solutions in $\mathbb{L}^p$ for $p \in (1,2]$. Our results apply to generators that are stochastic monotone in the $y$-variable, stochastic Lipschitz in the $z$-variable, and satisfy a general stochastic linear growth condition. |
| title | $\mathbb{L}^p$-solution of generalized BSDEs in a general filtration with stochastic monotone coefficients |
| topic | Probability 60H05, 60H10, 34F05, 35R60, 60H30 |
| url | https://arxiv.org/abs/2501.15600 |