Inhomogeneous Lévy Processes in Lie Groups

Ming Liao
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Ming Liao: Auburn University, Department of Mathematics and Statistics

Chapter Chapter 6 in Invariant Markov Processes Under Lie Group Actions, 2018, pp 169-237 from Springer

Abstract: Abstract Inhomogeneous Lévy processes in topological groups, defined by independent increments, were introduced in § 1.4 . More useful representation of these processes may be obtained on a Lie group G. The main purpose of this chapter is to present a martingale representation, which characterizes an inhomogeneous Lévy process in a Lie group by a triple (b, A, η) of a deterministic path b t in G, called a drift, a matrix function A(t) and a measure function η(t, ⋅), in close analogy with the representation of a homogeneous Lévy process.

Date: 2018
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DOI: 10.1007/978-3-319-92324-6_6

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