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)

• Record Type: Journal Article
• Authors: Wang, Qianru; Liao, Junxia; Fan, Shengjun
• Is Part Of: Communications in statistics. Volume 48:Issue 7(2019)
• Page Start: 2099
• Page End: 2109
• Publication Date: 2019-08-09
• Subjects: Backward stochastic differential equation -- weak monotonicity -- comparison theorem -- linear growth -- uniform continuity; 60H10; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2018.1433842
• Languages: English
• ISSNs: 0361-0918

Abstract

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 .