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

[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.

[学科分类] 电力

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