On Diffusion Hemigroups of Probability Measures on an Abelian Locally Compact Group
- Resource Type
- Article
- Authors
- Bingham, M.; Heyer, H.
- Source
- Results in Mathematics; May 2000, Vol. 37 Issue: 3-4 p204-225, 22p
- Subject
- Language
- ISSN
- 14226383; 14209012
The connections are investigated between the diffusion property for a two-parameter semigroup (hemigroup) of probability measures on an abelian locally compact group, the vanishing of the Levy measure in the Lévy-Khinchine representation of the hemigroup, and the existence of a version of the increment process corresponding to the hemigroup that has continuous paths. These properties are shown to be equivalent if the hemigroup has a certain Lipschitz bounded variation property. The bounded variation property used here is compared with other notions of bounded variation that have been used in similar investigations for other types of groups.