Tohoku Mathematical Journal
- Tohoku Math. J. (2)
- Volume 59, Number 3 (2007), 401-422.
On the Feller property of Dirichlet forms generated by pseudo differential operators
We show that a large class of regular symmetric Dirichlet forms is generated by pseudo differential operators. We calculate the symbols which are closely related to the semimartingale characteristics (Lévy system) of the associated stochastic processes. Using the symbol we obtain estimates for the mean sojourn time of the process for balls. These estimates and a perturbation argument enable us to prove Hölder regularity of the resolvent and semigroup; this entails that the semigroup has the Feller property.
Tohoku Math. J. (2), Volume 59, Number 3 (2007), 401-422.
First available in Project Euclid: 11 October 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 31C25: Dirichlet spaces
Secondary: 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07] 60J75: Jump processes 60G52: Stable processes 47G30: Pseudodifferential operators [See also 35Sxx, 58Jxx]
Schilling, René L.; Uemura, Toshihiro. On the Feller property of Dirichlet forms generated by pseudo differential operators. Tohoku Math. J. (2) 59 (2007), no. 3, 401--422. doi:10.2748/tmj/1192117985. https://projecteuclid.org/euclid.tmj/1192117985