Lévy processes and Jacobi fields

Details Lévy processes and Jacobi fields Lévy processes and Jacobi fields

2004-07-22

arxiv.org/abs/math/0407377v2

Mathematics

Probability

Scientific paper

We review the recent results on the Jacobi field of a (real-valued) L\'evy process defined on a Riemannian manifold. In the case where the L\'evy process is neither Gaussian, nor Poisson, the corresponding Jacobi field acts in an extended Fock space. We also give a unitary equivalent representation of the Jacobi field in a usual Fock space. This representation is inspired by a result by Accardi, Franz, and Skeide (2002).

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