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Malliavin matrix of degenerate SDE and gradient estimate


 
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1. Title Title of document Malliavin matrix of degenerate SDE and gradient estimate
 
2. Creator Author's name, affiliation, country Zhao Dong; Chinese Academy of Sciences; China
 
2. Creator Author's name, affiliation, country Xuhui Peng; Hunan Normal University; China
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Degenerate stochastic differential equation; Gradient estimate; Strong Feller; Malliavin calculus; H\"{o}rmander condition
 
3. Subject Subject classification 60H10,60H07
 
4. Description Abstract In this article, we prove that the inverse of Malliavin matrix belongs to $L^p(\Omega,\mathbb{P})$ for a class of degenerate stochastic differential equation (SDE). The conditions required are similar to Hörmander's bracket condition, but we  don't need all coefficients of the SDE are smooth. Furthermore, we obtain a locally uniform estimate for the Malliavin matrix and a gradient estimate. We also prove that the semigroup generated by the SDE is strong Feller. These results are illustrated through examples.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Supported by 973 Program, No. 2011CB808000 and Key Laboratory of Random Complex Structures and Data Science, No.2008DP173182, NSFC, No.:10721101, 11271356, 11371041.
 
7. Date (YYYY-MM-DD) 2014-08-15
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/3120
 
10. Identifier Digital Object Identifier 10.1214/EJP.v19-3120
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 19
 
12. Language English=en en
 
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