Lévy processes and Jacobi fields

Eugene Lytvynov

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Lévy processes and Jacobi fields

Eugene Lytvynov

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Abstract

We review the recent results on the Jacobi field of a (real-valued) Lévy process defined on a Riemannian manifold. In the case where the Lévy 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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Eugene Lytvynov. 2005-03-09. Lévy processes and Jacobi fields. https://arxiv.org/abs/math/0407377

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