Multi-dimensional Backward Stochastic Differential Equations of Diagonally Quadratic Generators with a Special Structure

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 not equal i). Finally, a solvability result is given when the diagonally quadratic generator is triangular.