On a Class of Non-Translation Invariant Feller Semigroups on Lie Groups |
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Authors: | Applebaum David |
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Institution: | (1) Department of Mathematics, Statistics and Operational Research, Nottingham Trent University, Burton Street, NG1 4BU Nottingham, England, UK |
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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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Keywords: | Feller semigroup Hunt's formula Hunt function Lé vy kernel Ornstein– Uhlenbeck process hypoellipticity |
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