{"title":"一类退化稳定驱动SDEs的参数化方法","authors":"Lorick Huang, S. Menozzi","doi":"10.1214/15-AIHP704","DOIUrl":null,"url":null,"abstract":"We consider a stable driven degenerate stochastic differential equation, whose coefficients satisfy a kind of weak Hormander condition. Under mild smoothness assumptions we prove the uniqueness of the martingale problem for the associated generator under some dimension constraints. Also, when the driving noise is scalar and tempered, we establish density bounds reflecting the multi-scale behavior of the process.","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"87 1","pages":"1925-1975"},"PeriodicalIF":1.2000,"publicationDate":"2014-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"25","resultStr":"{\"title\":\"A parametrix approach for some degenerate stable driven SDEs\",\"authors\":\"Lorick Huang, S. Menozzi\",\"doi\":\"10.1214/15-AIHP704\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider a stable driven degenerate stochastic differential equation, whose coefficients satisfy a kind of weak Hormander condition. Under mild smoothness assumptions we prove the uniqueness of the martingale problem for the associated generator under some dimension constraints. Also, when the driving noise is scalar and tempered, we establish density bounds reflecting the multi-scale behavior of the process.\",\"PeriodicalId\":7902,\"journal\":{\"name\":\"Annales De L Institut Henri Poincare-probabilites Et Statistiques\",\"volume\":\"87 1\",\"pages\":\"1925-1975\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2014-02-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"25\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales De L Institut Henri Poincare-probabilites Et Statistiques\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1214/15-AIHP704\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1214/15-AIHP704","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
A parametrix approach for some degenerate stable driven SDEs
We consider a stable driven degenerate stochastic differential equation, whose coefficients satisfy a kind of weak Hormander condition. Under mild smoothness assumptions we prove the uniqueness of the martingale problem for the associated generator under some dimension constraints. Also, when the driving noise is scalar and tempered, we establish density bounds reflecting the multi-scale behavior of the process.
期刊介绍：
The Probability and Statistics section of the Annales de l’Institut Henri Poincaré is an international journal which publishes high quality research papers. The journal deals with all aspects of modern probability theory and mathematical statistics, as well as with their applications.
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