Abstract
An (unbounded) operator Ξ on Boson Fock space over L 2(R +) is called regular if it is an admissible white noise operator such that the conditional expectations give rise to a regular quantum martingale. We prove that an admissible white noise operator is regular if and only if it admits a quantum stochastic integral representation.
Mathematics Subject Classification (2000):
Acknowledgements
This article was supported by the Korea–Japan Basic Scientific Cooperation Program (2007–2009) “Noncommutative Stochastic Analysis and Its Applications to Network Science.”