An equivalent representation of the Jacobi field of a Lévy process

Details An equivalent representation of the Jacobi field of a Lévy process An equivalent representation of the Jacobi field of a Lévy process

2005-01-25

arxiv.org/abs/math/0501450v1

Mathematics

Probability

Scientific paper

In [Yu.M. Berezansky, E. Lytvynov, D. A. Mierzejewski, Ukrainian Math. J. 55 (2003), 853--858 ], the Jacobi field of a L\'evy process was derived. This field consists of commuting self-adjoint operators acting in an extended (interacting) Fock space. However, these operators have a quite complicated structure. In this note, using ideas from [L. Accardi. U. Franz, M. Skeide, Comm. Math. Phys. 228 (2002), 123--150] and [E. Lytvynov, Infin. Dimen. Anal. Quant. Prob. Rel. Top. 7 (2004), 619--629], we obtain a unitary equivalent representation of the Jacobi field of a L\'evy process. In this representation, the operators act in a usual symmetric Fock space and have a much simpler structure.

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