Invariant measures of symmetric Lévy processes
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- by Jiangang Ying PDF
- Proc. Amer. Math. Soc. 120 (1994), 267-273 Request permission
Abstract:
If $\pi = \{ {\pi _t}:t > 0\}$ is a symmetric convolution semigroup with the Lévy exponent $\phi$, then supp ${\pi _t}$, is a group determined by $\phi$, and $\pi$ has a unique Radon invariant measure if and only if $\phi$ has a unique zero at $0$.References
- Christian Berg and Gunnar Forst, Potential theory on locally compact abelian groups, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 87, Springer-Verlag, New York-Heidelberg, 1975. MR 0481057, DOI 10.1007/978-3-642-66128-0
- R. M. Blumenthal and R. K. Getoor, Markov processes and potential theory, Pure and Applied Mathematics, Vol. 29, Academic Press, New York-London, 1968. MR 0264757
- Gustave Choquet and Jacques Deny, Sur l’équation de convolution $\mu =\mu \ast \sigma$, C. R. Acad. Sci. Paris 250 (1960), 799–801 (French). MR 119041
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 120 (1994), 267-273
- MSC: Primary 60J30
- DOI: https://doi.org/10.1090/S0002-9939-1994-1200181-3
- MathSciNet review: 1200181