Multi-Dimensional Backward Stochastic Differential Equations of Diagonally Quadratic generators

Published 20 Aug 2014 in math.PR | (1408.4579v1)

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 H\"older inequalities for BMO martingales.

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