标题：An exploration of L-p-theory for forward-backward stochastic differential equations with random coefficients on small tor durations
作者：Xie, Bing; Yu, Zhiyong
作者机构：[Xie, Bing; Yu, Zhiyong] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China.
通讯作者地址：[Yu, ZY]Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China.
来源：JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
关键词：Forward-backward stochastic differential equation; Random coefficient;; L-p-theory; Small duration; Global implicit function theorem
摘要：In the present paper, under the Lipschitz condition and a monotonicity assumption, we obtain an L-p-result (p > 1), including the existence and uniqueness of the p-th power integrable solutions and a pair of related p-th power estimates, for coupled forward-backward stochastic differential equations with random coefficients on small durations. A measurable global implicit function theorem has been established and plays a key role in our analysis. It is the first measurable version of implicit function theorems to our best knowledge, therefore the theorems themselves have been improved. (C) 2019 Elsevier Inc. All rights reserved.