q-Levy processes Institutional Repository Document uri icon

abstract

  • We continue the investigation of the Levy processes on a q-deformed full Fock space started in a previous paper. First, we show that the vacuum vector is cyclic and separating for the algebra generated by such a process. Next, we describe a chaotic representation property in terms of multiple integrals with respect to diagonal measures, in the style of Nualart and Schoutens. We define stochastic integration with respect to these processes, and calculate their combinatorial stochastic measures. Finally, we show that they generate infinite von Neumann algebras.

author list (cited authors)

  • Anshelevich, M.

citation count

  • 0

complete list of authors

  • Anshelevich, Michael

Book Title

  • arXiv

publication date

  • September 2003