Lévy Processes in Homogeneous Spaces

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

Chapter Chapter 3 in Invariant Markov Processes Under Lie Group Actions, 2018, pp 73-101 from Springer

Abstract: Abstract Hunt’s generator formula for Lévy processes in a Lie group G holds also for Lévy processes in a homogeneous space G∕K, this will be discussed in §3.2, and some preparation will be dealt with in §3.1. Using this formula, it will be shown in §3.3 that a Lévy process in G∕K may be obtained as a projection of a Lévy process in G. As an application, some results on convolution semigroups on G and on G∕K will be derived in §3.4. In §3.4, we will also consider the problem of embedding an infinitely divisible distribution in a continuous convolution semigroup. A special class of Lévy processes in G or G∕K are Riemannian Brownian motions. Some related stochastic differential equations, and relations between Brownian motions in G and in G∕K, will be considered in §3.5.

Date: 2018
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DOI: 10.1007/978-3-319-92324-6_3

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