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 ( 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...
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| Date: | 2003 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2003
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| Series: | Український математичний журнал |
| Subjects: | |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | The Jacobi Field of a Lévy Process / Yu.M. Berezansky, E. Lytvynov, D.A. Mierzejewski // Український математичний журнал. — 2003. — Т. 55, № 5. — С. 706–710. — Бібліогр.: 18 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | We derive an explicit formula for the Jacobi field that is acting in an extended Fock space and corresponds to an ( 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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