$\mathbb{L}^p$ $(p>1)$-solutions for BSDEs with jumps and stochastic monotone generator
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| Format: | Preprint |
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2025
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| _version_ | 1866917908444086272 |
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| author | Elmansouri, Badr Otmani, Mohamed El |
| author_facet | Elmansouri, Badr Otmani, Mohamed El |
| contents | We study multidimensional discontinuous backward stochastic differential equations in a filtration that supports both a Brownian motion and an independent integer-valued random measure. Under suitable $\mathbb{L}^p$-integrability conditions on the data, we establish the existence and uniqueness of $\mathbb{L}^p$-solutions for both cases: $p \geq 2$ and $p \in (1,2)$. The generator is assumed to be stochastically monotone in the state variable $y$, stochastically Lipschitz in the control variables $(z, u)$, and to satisfy a stochastic linear growth condition, along with an appropriate $\mathbb{L}^p$-integrability requirement. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00371 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $\mathbb{L}^p$ $(p>1)$-solutions for BSDEs with jumps and stochastic monotone generator Elmansouri, Badr Otmani, Mohamed El Probability 60H10, 60H15, 60H30 We study multidimensional discontinuous backward stochastic differential equations in a filtration that supports both a Brownian motion and an independent integer-valued random measure. Under suitable $\mathbb{L}^p$-integrability conditions on the data, we establish the existence and uniqueness of $\mathbb{L}^p$-solutions for both cases: $p \geq 2$ and $p \in (1,2)$. The generator is assumed to be stochastically monotone in the state variable $y$, stochastically Lipschitz in the control variables $(z, u)$, and to satisfy a stochastic linear growth condition, along with an appropriate $\mathbb{L}^p$-integrability requirement. |
| title | $\mathbb{L}^p$ $(p>1)$-solutions for BSDEs with jumps and stochastic monotone generator |
| topic | Probability 60H10, 60H15, 60H30 |
| url | https://arxiv.org/abs/2502.00371 |