Salvato in:
| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2603.14447 |
| Tags: |
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Sommario:
- 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.