{"title":"On strong solutions of Itô’s equations with Dσ and b in Morrey classes containing Ld","authors":"N.V. Krylov","doi":"10.1214/23-aop1630","DOIUrl":null,"url":null,"abstract":"We consider Itô uniformly nondegenerate equations with time independent coefficients, the diffusion coefficient in W2+ε,loc1, and the drift in a Morrey class containing Ld. We prove the unique strong solvability in the class of admissible solutions for any starting point. The result is new even if the diffusion is constant.","PeriodicalId":50763,"journal":{"name":"Annals of Probability","volume":null,"pages":null},"PeriodicalIF":2.1000,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1214/23-aop1630","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 4
Abstract
We consider Itô uniformly nondegenerate equations with time independent coefficients, the diffusion coefficient in W2+ε,loc1, and the drift in a Morrey class containing Ld. We prove the unique strong solvability in the class of admissible solutions for any starting point. The result is new even if the diffusion is constant.
期刊介绍：
The Annals of Probability publishes research papers in modern probability theory, its relations to other areas of mathematics, and its applications in the physical and biological sciences. Emphasis is on importance, interest, and originality – formal novelty and correctness are not sufficient for publication. The Annals will also publish authoritative review papers and surveys of areas in vigorous development.
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