The Jacobi Field of a Lévy Process

  • Yu. M. Berezansky
  • E. V. Lytvynov
  • D. A. Mierzejewski


We derive an explicit formula for the Jacobi field that is acting in an extended Fock space and corresponds to an ( \(\mathbb{R}\) -valued) Lévy process on a Riemannian manifold. The support of the measure of jumps in the Lévy–Khintchine representation for the Lévy process is supposed to have an infinite number of points. We characterize the gamma, Pascal, and Meixner processes as the only Lévy process whose Jacobi field leaves the set of finite continuous elements of the extended Fock space invariant.
How to Cite
Berezansky, Y. M., E. V. Lytvynov, and D. A. Mierzejewski. “The Jacobi Field of a Lévy Process”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 55, no. 5, May 2003, pp. 706-10,
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