Multi-dimensional backward stochastic differential equations of diagonally quadratic generators with a special structure (Q6655121)

This paper focuses on establishing the well-posedness of a class of multi-dimensional backward stochastic differential equations (BSDEs) with a diagonally quadratic generator. A novel a priori estimate is introduced, and it is demonstrated that the BSDE possesses a unique solution over a specified interval, provided the generator exhibits sufficiently small growth in its off-diagonal elements (specifically, for each \(i\), the \(i\)-th component of the generator depends on the \(j\)-th row \(z_j\) of the variable \(z\) with limited growth for \(j \neq i\)). Additionally, a solvability result is presented for the case where the diagonally quadratic generator is triangular.