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 ℝd and its extension to Lie groups.
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Acknowledgements
Helpful comments from David Applebaum and an anonymous referee have led to a considerable improvement of the exposition.
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Liao, M. Inhomogeneous Lévy Processes in Lie Groups and Homogeneous Spaces. J Theor Probab 27, 315–357 (2014). https://doi.org/10.1007/s10959-012-0415-6
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DOI: https://doi.org/10.1007/s10959-012-0415-6