Backward doubly stochastic differential equations with or without reflection under weak conditions
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866908887755522048 |
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| author | Gao, Shuxian Hu, Ying Wen, Jiaqiang |
| author_facet | Gao, Shuxian Hu, Ying Wen, Jiaqiang |
| contents | In this paper, we study the well-posedness of backward doubly stochastic differential equations (BDSDEs), both with and without reflection, under weak conditions. First, when the generator $f$ is of general growth in $y$ and linear growth in $z$, we establish the existence, uniqueness, comparison principle, and the existence of maximal solutions for BDSDEs, with or without reflection. Second, under the assumption that $f$ is of linear growth in $y$ and quadratic growth in $z$, and that the terminal value is bounded, we prove the existence, uniqueness, and comparison principle for reflected and non-reflected BDSDEs. Finally, when the generator $f$ is of general growth in $y$ and quadratic growth in $z$, again with a bounded terminal value, we prove the existence of maximal solutions for BDSDEs in both the reflected and non-reflected situations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14447 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Backward doubly stochastic differential equations with or without reflection under weak conditions Gao, Shuxian Hu, Ying Wen, Jiaqiang Probability 60H10, 60H20 In this paper, we study the well-posedness of backward doubly stochastic differential equations (BDSDEs), both with and without reflection, under weak conditions. First, when the generator $f$ is of general growth in $y$ and linear growth in $z$, we establish the existence, uniqueness, comparison principle, and the existence of maximal solutions for BDSDEs, with or without reflection. Second, under the assumption that $f$ is of linear growth in $y$ and quadratic growth in $z$, and that the terminal value is bounded, we prove the existence, uniqueness, and comparison principle for reflected and non-reflected BDSDEs. Finally, when the generator $f$ is of general growth in $y$ and quadratic growth in $z$, again with a bounded terminal value, we prove the existence of maximal solutions for BDSDEs in both the reflected and non-reflected situations. |
| title | Backward doubly stochastic differential equations with or without reflection under weak conditions |
| topic | Probability 60H10, 60H20 |
| url | https://arxiv.org/abs/2603.14447 |