Abstract
The study of symmetric property in the L 2-sense for the non-positive definite operator is motivated by the theory of probability and analysis. This paper presents some sufficient conditions for the existence of symmetric measure for Lévy type operator. Some new examples are illustrated. The present study is an important step for considering various ergodic properties and functional inequalities of Lévy type operator.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Albeverio, S., Rüdiger, B., Wu, J. L.: Invariant measures and symmetry property of Lévy type operators. Potential Analysis, 13, 147–168 (2000)
Sato, K.: Lévy Processes and Infinity Divisible Distributions, Cambridge University Press, 1999
Chen, M. F., Wang, F. Y.: Estimation of spectral gap for elliptic operator. Trans. Amer. Math. Soc., 349,1239–1267 (1997)
Fukushima, M., Oshima, Y., Takeda, M.: Dirichlet Forms and Symmetric Markov Processes, de Gruyter, Stud. Math. Vol. 19, Berlin, 1994
Chen, M. F.: From Markov Chains to Non-Equilibrium Particle Systems, World Scientific, Singapore, 2nd, 2004
Schilling, R. L., Uemura, T.: Dirichlet forms generated by pseudo differential operators: on the Feller property of the associated stochastic processes. Tohoku Math. J., 59, 401–422 (2007)
Author information
Authors and Affiliations
Corresponding author
Additional information
Research supported in part by NSFC (No. 10271207)
Rights and permissions
About this article
Cite this article
Wang, J. Symmetric Lévy type operator. Acta. Math. Sin.-English Ser. 25, 39–46 (2009). https://doi.org/10.1007/s10114-008-7154-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10114-008-7154-8