@article{Berezansky_Lytvynov_Mierzejewski_2003, title={The Jacobi Field of a Lévy Process}, volume={55}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/3945}, abstractNote={We derive an explicit formula for the Jacobi field that is acting in an extended Fock space and corresponds to an (<span class="a-plus-plus inline-equation id-i-e1"> <span class="a-plus-plus equation-source format-t-e-x"> \(\mathbb{R}\) </span> </span>-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.}, number={5}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Berezansky, Yu. M. and Lytvynov, E. V. and Mierzejewski, D. A.}, year={2003}, month={May}, pages={706-710} }