The Jacobi Field of a Lévy Process
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...
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| Дата: | 2003 |
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| Автори: | , , , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2003
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/3945 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | 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. |
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