The reverse Hölder inequality for matrix-valued stochastic exponentials and applications to quadratic BSDE systems

In this paper, we study the connections between three concepts — reverse Hölder inequality for matrix-valued martingales, well-posedness of linear BSDEs with unbounded coefficients, and quadratic BSDE systems. particular, show that a bmo coefficients is well-posed if only stochastic exponential related martingale satisfies inequality. Furthermore, give structural conditions under which these equivalent are satisfied. Finally, apply our results on equations to obtain global two new classes non-Markovian systems special structure.