Quantum stochastic integral representations of Fock space operators

摘要

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 {M_t = E_tΞE_t} 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.