Skip to main content
Article thumbnail
Location of Repository

Some self-adjoint quantum semimartingales

By Alexander C. R. Belton


It is proved that the quantum stochastic gauge integral preserves self-adjointness of vacuum-adapted processes. This fact, together with bounded perturbations and the link between the Hudson–Parthasarathy calculus and vacuum-adapted theory, is used to produce many self-adjoint quantum semimartingales

Year: 2006
OAI identifier:
Provided by: Lancaster E-Prints

Suggested articles


  1. (1998). A matrix formulation of quantum stochastic calculus’, DPhil Thesis,
  2. (1994). An algebra of non-commutative bounded semimartingales: square and angle quantum brackets’, doi
  3. (2004). An isomorphism of quantum semimartingale algebras’, doi
  4. (1998). Extensions of quantum stochastic calculus’, Quantum probability communications XI, Grenoble summer school, doi
  5. (2001). Filtered stochastic calculus’, doi
  6. (1957). Functional analysis and semi-groups, revised edn,
  7. (1991). Functional analysis, 2nd edn (McGraw-Hill,
  8. (1980). Functional analysis, 6th edn (Springer, doi
  9. (1997). Fundamentals of the theory of operator algebras II: advanced theory, doi
  10. (1972). Methods of modern mathematical physics I: functional analysis doi
  11. (1975). Methods of modern mathematical physics II: Fourier analysis, selfadjointness
  12. (1978). Methods of modern mathematical physics IV: analysis of operators doi
  13. (1995). Probability and measure, 3rd edn
  14. (1984). Quantum Ito’s formula and stochastic evolutions’, doi
  15. (2005). Quantum stochastic analysis – an introduction’, Quantum independent increment processes I (eds M. doi
  16. (1987). Quantum stochastic calculus for Hilbert Schmidt processes’, Stochastic analysis, path integration and dynamics,
  17. (2001). Quantum Ω-semimartingales and stochastic evolutions’, doi
  18. (1987). Real and complex analysis, 3rd edn (McGraw-Hill,
  19. (2002). The Poisson process in quantum stochastic calculus’, DPhil Thesis,
  20. (1961). Theory of linear operators in Hilbert space I (Frederick Ungar, doi
  21. (2000). Vincent-Smith,‘ T h eI t ˆ o formula for perturbed Brownian martingales’, doi
  22. (1997). Vincent-Smith,‘ T h eI t ˆ o formula for quantum semimartingales’, doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.