Multiple Q-Adapted Integrals and Ito Formula of Noncommutative   Stochastic Calculus in Fock Space
  We study the continuity property of multiple Q-adapted quantum stochastic integrals with respect to noncommuting integrands given by the non-adapted multiple integral kernels in Fock scale. The noncommutative algebra of relatively (exponentially) bounded nonadapted quantum stochastic processes is studied in the kernel form as introduced by Belavkin in 1991. The differential Q-adapted formula generalizing Ito product formula for adapted integrals is presented in both strong and weak sense as a particular case of the quantum stochastic nonadapted Ito formula. 
Viacheslav P. Belavkin and Matthew F. Brown
math-ph math.MP math.QA quant-ph