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Journal of Theoretical Probability

, Volume 27, Issue 2, pp 315–357 | Cite as

Inhomogeneous Lévy Processes in Lie Groups and Homogeneous Spaces

  • Ming Liao
Article

Abstract

We obtain a representation of an inhomogeneous Lévy process in a Lie group or a homogeneous space in terms of a drift, a matrix function and a measure function. Since the stochastic continuity is not assumed, our result generalizes the well-known Lévy–Itô representation for stochastic continuous processes with independent increments in ℝ d and its extension to Lie groups.

Keywords

Lévy processes Lie groups Homogeneous spaces 

Mathematics Subject Classification

60J25 58J65 

Notes

Acknowledgements

Helpful comments from David Applebaum and an anonymous referee have led to a considerable improvement of the exposition.

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsAuburn UniversityAuburnUSA

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