On Weak Uniqueness for Some Degenerate SDEs by Global L p Estimates

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• 作者：Enrico Priola
• 关键词：Ornstein ; Uhlenbeck processes ; Degenerate stochastic differential equations ; Well ; posedness of martingale problem ; Localization principle ; 60H10 ; 60J60 ; 35J70
• 刊名：Potential Analysis
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：42
• 期：1
• 页码：247-281
• 全文大小：679 KB
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• 作者单位：Enrico Priola (1)
  
  1. Department of Mathematics, University of Torino, via Carlo Alberto 10, Torino, Italy
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Potential Theory
  Probability Theory and Stochastic Processes
  Geometry
  Functional Analysis
  
• 出版者：Springer Netherlands
• ISSN：1572-929X

文摘

We prove uniqueness in law for possibly degenerate SDEs having a linear part in the drift term. Diffusion coefficients corresponding to non-degenerate directions of the noise are assumed to be continuous. When the diffusion part is constant we recover the classical degenerate Ornstein-Uhlenbeck process which only has to satisfy the H?rmander hypoellipticity condition. In the proof we also use global L p -estimates for hypoelliptic Ornstein-Uhlenbeck operators recently proved in Bramanti et al. (Math. Z. 266, 789-16 2010) and adapt the localization procedure introduced by Stroock and Varadhan. Appendix contains a quite general localization principle for martingale problems.