{"title":"Mimicking and Conditional Control with Hard Killing","authors":"Rene Carmona, Daniel Lacker","doi":"arxiv-2409.10650","DOIUrl":null,"url":null,"abstract":"We first prove a mimicking theorem (also known as a Markovian projection\ntheorem) for the marginal distributions of an Ito process conditioned to not\nhave exited a given domain. We then apply this new result to the proof of a\nconjecture of P.L. Lions for the optimal control of conditioned processes.","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"32 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10650","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We first prove a mimicking theorem (also known as a Markovian projection
theorem) for the marginal distributions of an Ito process conditioned to not
have exited a given domain. We then apply this new result to the proof of a
conjecture of P.L. Lions for the optimal control of conditioned processes.
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