Malliavin and flow regularity of SDEs. Application to the study of densities and the stochastic transport equation

被引：4

作者：

Banos, David ^{[1
]}

Nilssen, Torstein ^{[1
]}

机构：

[1] Univ Oslo, Dept Math, CMA, Oslo, Norway

来源：

STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES | 2016年 / 88卷 / 04期

关键词：

Strong solutions of SDEs; Malliavin regularity; Sobolev regularity; regularity of densities; stochastic transport equation;

D O I：

10.1080/17442508.2015.1102265

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work we present a condition for the regularity, in both space and Malliavin sense, of strong solutions to SDEs driven by Brownian motion. We conjecture that this condition is optimal. As a consequence, we are able to improve the regularity of densities of such solutions. We also apply these results to construct a classical solution to the stochastic transport equation when the drift is Lipschitz.

引用

页码：540 / 566

页数：27

共 20 条

[1] On differentiability of stochastic flow for a multidimensional SDE with discontinuous drift [J].