English

Multiple Q-Adapted Integrals and Ito Formula of Noncommutative Stochastic Calculus in Fock Space

Mathematical Physics 2011-12-02 v1 math.MP Quantum Algebra Quantum Physics

Abstract

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.

Keywords

Cite

@article{arxiv.1112.0159,
  title  = {Multiple Q-Adapted Integrals and Ito Formula of Noncommutative Stochastic Calculus in Fock Space},
  author = {Viacheslav P. Belavkin and Matthew F. Brown},
  journal= {arXiv preprint arXiv:1112.0159},
  year   = {2011}
}

Comments

Due to appear in communications on stochastic analysis journal (KRP volume). 21 pages