Abstract
We consider a class of Feller semigroups on Lie groups which fail to commute with left translation due to the existence of a cocycle h which is identically one for Lévy processes. Under certain conditions, we are able to show that the infinitesimal generator of such a semigroup has the Lévy–Khintchine–Hunt form but with variable characteristics, thus we obtain an extension of classical work in Euclidean space by Courrège.
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Applebaum, D. On a Class of Non-Translation Invariant Feller Semigroups on Lie Groups. Potential Analysis 16, 103–114 (2002). https://doi.org/10.1023/A:1012656604378
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DOI: https://doi.org/10.1023/A:1012656604378