一类随机格朗沃尔不等式及其应用。
A class of stochastic Gronwall's inequality and its application.
作者信息
Wang Xin, Fan Shengjun
机构信息
School of Mathematics, China University of Mining and Technology, Xuzhou, China.
出版信息
J Inequal Appl. 2018;2018(1):336. doi: 10.1186/s13660-018-1932-3. Epub 2018 Dec 10.
Abstract
This paper puts forward the basic form of stochastic Gronwall's inequality and uses, respectively, the iterative method, the integral method and the martingale representation method to prove it. Then it presents an application to prove a comparison theorem of solutions for one-dimensional backward stochastic differential equations under the stochastic Lipschitz condition.
摘要
本文提出了随机格朗沃尔不等式的基本形式，并分别用迭代法、积分法和鞅表示法对其进行了证明。然后给出一个应用，用以证明在随机利普希茨条件下一维倒向随机微分方程解的一个比较定理。
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