On the comparison theorem for multidimensional BSDEs

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Necessary and sufficient condition for comparison theorem of 1-dimensional stochastic differential equations (2006, background): “This approach can also be applied to multi-dimensional situation (see [6]).”
Switching problem and related system of reflected backward SDEs (2010, methodology): “We note that one can also use the comparison theorem for high-dimensional BSDEs, see [25], to prove the monotonicity of Y n, j .”
7 – Backward Stochastic Differential Equations (2011, unknown): “In 2006, Hu and Peng [47] published a short article about the necessary and sufficient conditions for the existence of the multidimensional comparison theorem.”
A class of globally solvable Markovian quadratic BSDE systems and applications (2016, background): “Partial-regularity and hole-filling techniques can be seen as a replacement for order-based arguments involving, for instance, the maximum principle (comparison principle) or the related notion of a viscosity solution; such methods, unfortunately, fail miserably in the multidimensional case (see [36”