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≠i).Finally,a solvability result is given when the diagonally quadratic generator is triangular.
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