Multi-Dimensional Backward Stochastic Differential Equations of Diagonally Quadratic generators
arXiv:1408.4579
Abstract
The paper is concerned with adapted solution of a multi-dimensional BSDE with a "diagonally" quadratic generator, the quadratic part of whose $i$th component only depends on the $i$th row of the second unknown variable. Local and global solutions are given. In our proofs, it is natural and crucial to apply both John-Nirenberg and reverse Hölder inequalities for BMO martingales.
17 pages