m-Dissipativity for Kolmogorov Operator of a Fractional Burgers Equation with Space-time White Noise

详细信息    查看全文

• 作者：Desheng Yang
• 关键词：Kolmogorov operator ; m ; dissipativity ; Core ; Fractional stochastic Burgers equation
• 刊名：Potential Analysis
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：44
• 期：2
• 页码：215-227
• 全文大小：261 KB
• 参考文献：1.Brzeźniak Z., Debbi L.: On Stochastic Burgers Equation Driven by a Fractional Power of the Laplacian and space-time white noise. Stochastic Differential Equation: Theory and Applications, Avolume in Honor of Professor Boris L. Rozovskii. In: Baxendale, P.H., Lototsky, S.V. (eds.) , pp 135–167 (2007)
  2.Brzeźiak Z., Debbi L., Goldys B.: Ergodic properties of fractional stochastic Burgers Equation. Glob. Stoch. Anal. 1(2), 149–174 (2011)
  3.Da Prato, G., Zabczyk, J.: Ergodicity for infinite dimensional systems. Cambridge University Press, Cambridge (1996)CrossRef MATH
  4.Da Prato, G., Debussche, A.: m-dissipativity of Kolmogorov operators corresponding to Burgers equations with space-time white noise. Potential Anal. 26(1), 31–55 (2007)CrossRef MathSciNet MATH
  5.Da Prato, G.: Transition semigroups correponding to Lipschitz dissipative systems. Discr. Contin. Dyn. Syst. 10(1&2), 177–192 (2004)MATH
  6.Da Prato, G., Zabczyk, J.: Differentiability of the Feynman-Kac semigroup and a control application. Rend. Mat. Accad. Lincei 9(8), 183–188 (1997)
  7.Hairer, M.: An introduction to stochastic PDEs. http://​www.​hairer.​org/​Teaching.​html . Unpublished lecture notes (2009)
  
• 作者单位：Desheng Yang (1)
  
  1. School of Mathematics and Statistics, Central South University, Changsha, 410083, China
  
• 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

This paper is concerned with the essential m-dissipativity of the Kolmogorov operator associated with a fractional stochastic Burgers equation with space-time white noise. Some estimates on the solution and its moments with respect to the invariant measure are given. Moreover we also study the smoothing properties of the transition semigroup and the corresponding fractional Ornstein-Uhlenbeck operator by introducing an auxiliary semigroup and (generalized) Bismut-Elworthy formula. From these results, we prove that the Kolmogorov operator of the problem is m-dissipative and the domain of the infinitesimal generator of the fractional Ornstein-Uhlenbeck operator is a core.