Multi-dimensional Backward Stochastic Differential Equations of Diagonally Quadratic Generators with a Special Structure
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911841088700416 |
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| author | Yang, Guang |
| author_facet | Yang, Guang |
| contents | The present paper is devoted to the well-posedness of a type of multi-dimensional backward stochastic differential equations (BSDEs) with a diagonally quadratic generator. We give a new priori estimate, and prove that the BSDE admits a unique solution on a given interval when the generator has a sufficiently small growth of the off-diagonal elements (i.e., for each $i$, the $i$-th component of the generator has a small growth of the $j$-th row $z^j$ of the variable $z$ for each $j \neq i$). Finally, we give a solvability result when the diagonally quadratic generator is triangular. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_12470 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Multi-dimensional Backward Stochastic Differential Equations of Diagonally Quadratic Generators with a Special Structure Yang, Guang Probability 60H10 The present paper is devoted to the well-posedness of a type of multi-dimensional backward stochastic differential equations (BSDEs) with a diagonally quadratic generator. We give a new priori estimate, and prove that the BSDE admits a unique solution on a given interval when the generator has a sufficiently small growth of the off-diagonal elements (i.e., for each $i$, the $i$-th component of the generator has a small growth of the $j$-th row $z^j$ of the variable $z$ for each $j \neq i$). Finally, we give a solvability result when the diagonally quadratic generator is triangular. |
| title | Multi-dimensional Backward Stochastic Differential Equations of Diagonally Quadratic Generators with a Special Structure |
| topic | Probability 60H10 |
| url | https://arxiv.org/abs/2302.12470 |