The Jacobi Field of a Lévy Process

• Date: 2003
• Main Authors: Berezansky, Yu. M., Lytvynov, E. V., Mierzejewski, D. A., Березанський, Ю. М., Литвинов, Є. В., Мерзєєвський, Д. А.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2003
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3945
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 i...