2005/01/25 by Eugene Lytvynov, Lytvynov, Eugene
Economics, Econometrics and Finance · Mathematics · #Mathematical functions and polynomials #Point processes and geometric inequalities #Stochastic processes and financial applications #math.FA #math.PR #msc:47B36 #msc:60G20 #msc:60G51 #msc:60H40
paper · pdf · doi:10.48550/arxiv.math/0501450
arxiv created 2005/01/25 · arxiv updated 2009/12/01
In [Yu.M. Berezansky, E. Lytvynov, D. A. Mierzejewski, Ukrainian Math. J. 55 (2003), 853--858 ], the Jacobi field of a Lévy 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 Lévy process. In this representation, the operators act in a usual symmetric Fock space and have a much simpler structure.