BURKHOLDER-DAVIS-GUNDY INEQUALITY FOR g-MARTINGALES.

In this study, we establish a Burkholder-Davis-Gundy (BDG) inequality type for certain nonlinear martingales arising from backward stochastic differential equations (BSDE) with generalized Lipschitz generator. As a consequence, we attempt to prove the equivalence between the convergence in probability of a g-martingale sequence and the associated quadratic variation sequence. Using a counterexample, we prove that BDG fails when g is quadratic. [ABSTRACT FROM AUTHOR]