L p solutions of finite and infinite time interval BSDEs with non-Lipschitz coefficients

Abstract

In this paper, we are interested in solving multidimensional backward stochastic differential equations (BSDEs) in under weaker assumptions on the coefficients, considering both a finite and an infinite time interval. We establish a general existence and uniqueness result of solutions in to finite and infinite time interval BSDEs with non-Lipschitz coefficients, which includes the corresponding results in Pardoux and Peng [Syst. Control Lett. 14 (1990), pp. 55–61], Mao [Stoch. Proc. Appl. 58 (1995), pp. 281–292], Chen and Wang [Chin. Sci. Bull. 42 (1997), pp. 2379–2383], Constantin [Analele Universităţii din Timişoara, Seria Matematică-Informatică XXXIX (2001), pp. 15–22], Wang and Wang [Chin. J. Appl. Probab. Statist. 19 (2003), pp. 245–251], Chen and Wang [J. Austral. Math. Soc. (Ser. A) 69 (2000), pp. 187–211] and Wang and Huang [Stat. Probability Lett. 79 (2009), pp. 1438–1443] as its particular cases.