{"title":"零反射正实线上扩散局部时间的正则性","authors":"Masafumi Hayashi","doi":"10.31390/COSA.13.1.02","DOIUrl":null,"url":null,"abstract":"We study the joint law of (Xt(x), Lt(x)) where Xt(x) is the solution of a one dimensional stochastic differential equation on (0,+∞) with reflection at zero, and Lt(x) is its local time. In particular, we give some representation formula of the distribution of (Xt(x), Lt(x)), and we investigate the regularity of the joint density with respect to the local time argument under ellipticity and mild regularity conditions on coefficients of Xt(x).","PeriodicalId":53434,"journal":{"name":"Communications on Stochastic Analysis","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Regularity of the Local Time of Diffusions on the Positive Real Line with Reflection at Zero\",\"authors\":\"Masafumi Hayashi\",\"doi\":\"10.31390/COSA.13.1.02\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the joint law of (Xt(x), Lt(x)) where Xt(x) is the solution of a one dimensional stochastic differential equation on (0,+∞) with reflection at zero, and Lt(x) is its local time. In particular, we give some representation formula of the distribution of (Xt(x), Lt(x)), and we investigate the regularity of the joint density with respect to the local time argument under ellipticity and mild regularity conditions on coefficients of Xt(x).\",\"PeriodicalId\":53434,\"journal\":{\"name\":\"Communications on Stochastic Analysis\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications on Stochastic Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.31390/COSA.13.1.02\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications on Stochastic Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31390/COSA.13.1.02","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
Regularity of the Local Time of Diffusions on the Positive Real Line with Reflection at Zero
We study the joint law of (Xt(x), Lt(x)) where Xt(x) is the solution of a one dimensional stochastic differential equation on (0,+∞) with reflection at zero, and Lt(x) is its local time. In particular, we give some representation formula of the distribution of (Xt(x), Lt(x)), and we investigate the regularity of the joint density with respect to the local time argument under ellipticity and mild regularity conditions on coefficients of Xt(x).
期刊介绍：
The journal Communications on Stochastic Analysis (COSA) is published in four issues annually (March, June, September, December). It aims to present original research papers of high quality in stochastic analysis (both theory and applications) and emphasizes the global development of the scientific community. The journal welcomes articles of interdisciplinary nature. Expository articles of current interest will occasionally be published. COSAis indexed in Mathematical Reviews (MathSciNet), Zentralblatt für Mathematik, and SCOPUS
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