Symmetry Groups and Translation Invariant Representations of Markov Processes
The symmetry groups of the potential theory of a Markov process Xtare used to introduce new algebraic and topological structures on the state space and the process. For example, let G be the collection of bijections φ on E which preserve the collection of excessive functions. Assume there is a trans...
| Veröffentlicht in: | The Annals of Probability. - Institute of Mathematical Statistics. - 19(1991), 2, Seite 562-586 |
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| 1. Verfasser: | |
| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
1991
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| Zugriff auf das übergeordnete Werk: | The Annals of Probability |
| Schlagworte: | Markov process potential theory topological groups Lie groups Mathematics Behavioral sciences Physical sciences |
| Zusammenfassung: | The symmetry groups of the potential theory of a Markov process Xtare used to introduce new algebraic and topological structures on the state space and the process. For example, let G be the collection of bijections φ on E which preserve the collection of excessive functions. Assume there is a transitive subgroup H of the symmetry group G such that the only map φ ∈ H fixing a point e ∈ E is the identity map on E. There is a bijection Ψ: E → H so that the algebraic structure of H can be carried to E, making E into a group. If there is a left quasi-invariant measure on E, then there is a topology on E making E into a locally compact second countable metric group. There is also a time change τ(t) of Xtsuch that Xτ(t)is a translation invariant process on E and Xτ(t)is right-continuous with left limits in the new topology. |
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| ISSN: | 00911798 |