MULTIDIMENSIONAL SDES WITH SINGULAR DRIFT AND UNIVERSAL CONSTRUCTION OF THE POLYMER MEASURE WITH WHITE NOISE POTENTIAL

• 成果类型: Article
• 署名作者: Cannizzaro, Giuseppe; Chouk, Khalil
• 署名单位: University of Warwick; Technical University of Berlin
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/17-AOP1213
• 发表日期: 2018
• 页码: 1710-1763
• 关键词: differential-equations

摘要

We study the existence and uniqueness of solution for stochastic differential equations with distributional drift by giving a meaning to the Stroock-Varadhan martingale problem associated to such equations. The approach we exploit is the one of paracontrolled distributions introduced in (Forum Math. Pi 3 ( 2015) e6). As a result, we make sense of the three-dimensional polymer measure with white noise potential.