A stochastic Gronwall inequality in random time horizon and its application to BSDE

Journal of inequalities and applications

article

Hun O¹  Mun-Chol Kim¹  Chol-Kyu Pak¹ 

[1] Faculty of Mathematics, Kim Il Sung University

关键词: Gronwall inequality;    Stochastic;    Random time horizon;    Backward stochastic differential equation;    Comparison;   

DOI  :  10.1186/s13660-020-2304-3

学科分类：电力

来源: SpringerOpen

【 摘 要 】

Gronwall’s inequality is a handy tool to derive many useful results such as uniqueness, comparison, boundedness, continuous dependence with respect to initial value, and stability in the theory of differential and integral equations. It was first introduced by Gronwall [9] as a differential form, and the integral inequality was proposed by Bellman [3]. Since then, many researchers have studied the various types of generalizations of this inequality motivated by the development of the differential and integral equations [1, 5, 7, 8, 12, 16, 19]. Among such generalizations, we are concerned with the stochastic version of Gronwall’s inequality.

【 授权许可】

CC BY