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| Multi-dimensional Backward Stochastic Differential Equations of DiagonallyQuadratic Generators with a Special Structure |
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Citation： |
Guang YANG.Multi-dimensional Backward Stochastic Differential Equations of DiagonallyQuadratic Generators with a Special Structure[J].Chinese Annals of Mathematics B,2024,45(6):855~868 |
| Page view： 444
Net amount： 168 |
Authors： |
Guang YANG; |
Foundation： |
the National Natural Science Foundation of China (Nos. 11631004,
12031009). |
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| Abstract： |
The present paper is devoted to the well-posedness of a type of multi-dimensional
backward stochastic differential equations (BSDE for short) with a diagonally quadratic
generator. The author gives 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 zj of the variable z for each j 6= i). Finally, a solvability result is
given when the diagonally quadratic generator is triangular. |
Keywords： |
Multi-dimensional BSDE, Diagonally quadratic generator, BMO
martingale |
Classification： |
60H10 |
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