平方可积系数随机微分方程强解的梯度估计  

Gradient Estimates of Strong Solutions for Stochastic Differential Equations with Square Integrable Drift

作　　者：魏金龙 吕广迎 Jinlong Wei;Guangying LÜ(School of Statistics and Mathematics,Zhongnan University of Economics and Law,Wuhan 430073,P.R.China;College of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,P.R.China)

机构地区：[1]中南财经政法大学统计与数学学院,武汉430073 [2]南京信息工程大学数学与统计学院,南京210044

出　　处：《数学学报(中文版)》2025年第2期350-368,共19页Acta Mathematica Sinica:Chinese Series

基　　金：国家自然科学基金(12171247,11971185);中南财经政法大学基本科研项目(112/31513111213)。

摘　　要：我们将Davie处理有界可测漂移系数随机微分方程的技巧(Int.Math.Res.Not.,2007,2007(1):1-26)推广到时间平方可积、空间H?lder连续漂移系数随机微分方程,得到了随机微分方程强解的梯度估计和一致局部拟Lipschitz估计.作为应用,我们得到了由Wiener噪声驱动的平方可积系数随机输运方程的唯一强可解性和随机强解的一致局部拟Lipschitz估计,并部分解决了Fedrizzi和Flandoli(J.Funct.Anal.,2013,264(6):1329-1354)提出的公开问题.We extend Davie's trick(it Int.Math.Res.Not.,2007,2007(1):1-26)from stochastic differential equations with bounded measurable drifts to the ones in which the drifts are square integrable in time variable and Hölder continuous in space variable,and obtain the gradient estimates as well as the uniformly local quasi-Lipschitz estimates for strong solutions.As applications,we prove the unique strong solvability for stochastic transport equations driven by Wiener noise with square integrable drift as well as the uniformly local quasi-Lipschitz estimates for stochastic strong solutions,which partially solves the open problem posed by Fedrizzi and Flandoli(J.Funct.Anal.,2013,264(6):1329-1354).

关 键 词：梯度估计 拟Lipschitz估计 强解 

分 类 号：O211.63[理学—概率论与数理统计]