Multi-Dimensional Backward Stochastic Differential Equations of Diagonally Quadratic generators
Abstract
The paper is concerned with adapted solution of a multi-dimensional BSDE with a "diagonally" quadratic generator, the quadratic part of whose ith component only depends on the ith 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 H\"older inequalities for BMO martingales.
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