Lp(1 < p ⩽ 2) solutions of one-dimensional BSDEs whose generator is weakly monotonic in y and non-Lipschitz in z. Issue 7 (9th August 2019) - Wang, Qianru; Liao, Junxia; Fan, Shengjun
ABSTRACT: In this paper, we start with establishing the existence of a minimal (maximal) L p (1 < p ⩽ 2) solution to a one-dimensional backward stochastic differential equation (BSDE), where the generator g satisfies a p -order weak monotonicity condition together with a general growth condition in y and a linear growth condition in z . Then, we propose and prove a comparison theorem of L p (1 < p ⩽ 2) solutions to one-dimensional BSDEs with q -order (1 ⩽ q < p ) weak monotonicity and uniform continuity generators. As a consequence, an existence and uniqueness result of L p (1 < p ⩽ 2) solutions is also given for BSDEs whose generator g is q -order (1 ⩽ q < p ) weakly monotonic with a general growth in y and uniformly continuous in z .