Weighted L p ( p ≥ 1) solutions of random time horizon BSDEs with stochastic monotonicity generators

In this paper, we are concerned with a multidimensional backward stochastic differential equation (BSDE) with a general random terminal time [Formula: see text], which may take values in [Formula: see text]. Firstly, we establish an existence and uniqueness result for a weighted [Formula: see text] solution of the preceding BSDE with generator [Formula: see text] satisfying a stochastic monotonicity condition with general growth in the first unknown variable [Formula: see text] and a stochastic Lipschitz continuity condition in the second unknown variable [Formula: see text]. Then, we derive an existence and uniqueness result for a weighted [Formula: see text] solution of the preceding BSDE under an additional stochastic sub-linear growth condition in [Formula: see text]. These results generalize the corresponding ones obtained in Li et al. [2024] to the [Formula: see text] solution case. Finally, the corresponding comparison theorems for the weighted [Formula: see text] solutions are also put forward and verified in the one-dimensional setting. In particular, we develop new ideas and systematical techniques in order to establish the above results.