Some self-adjoint quantum semimartingales

Proceedings of the London Mathematical Society

Volumn 92, Issue 3, 2006, Pages 791-816

  Belton, Alexander C R ^a,b  

^a UNIVERSITÉ LOUIS PASTEUR   (France)

^b UNIVERSITY COLLEGE CORK   (Ireland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33645978735     PISSN: 00246115     EISSN: 1460244X     Source Type: Journal    
DOI: 10.1017/S0024611505015650     Document Type: Article

References (22)

1. N. I. AKHIEZER and I. M. GLAZMAN, Theory of linear operators in Hilbert space I (Frederick Ungar, New York, 1961).
2. S. ATTAL, 'An algebra of non-commutative bounded semimartingales: square and angle quantum brackets', J. Funct. Anal. 124 (1994) 292-332.
3. S. ATTAL, 'Extensions of quantum stochastic calculus', Quantum probability communications XI, Grenoble summer school, 1998 (ed. S. Attal and J. M. Lindsay; World Scientific, Singapore, 2003) 1-37.
4. A. C. R. BELTON, 'A matrix formulation of quantum stochastic calculus', DPhil Thesis, University of Oxford, 1998.
5. A. C. R. BELTON, 'Quantum Ω-semimartingales and stochastic evolutions', J. Funct. Anal. 187 (2001) 94-109.
6. A. C. R. BELTON, 'An isomorphism of quantum semimartingale algebras', Q. J. Math. 55 (2004) 135-165.
7. P. BILLINGSLEY, Probability and measure, 3rd edn (John Wiley, New York, 1995).
8. E. HILLE and R. S. PHILLIPS, Functional analysis and semi-groups, revised edn, Colloquium Publications 31 (American Mathematical Society, Providence, RI, 1957).
9. R. L. HUDSON and P. KRÉE, 'Quantum stochastic calculus for Hilbert Schmidt processes', Stochastic analysis, path integration and dynamics, Warwick, 1987 (ed. K. D. Elworthy and J.-C. Zambrini), Pitman Research Notes in Mathematics 200 (Longman Scientific & Technical, Harlow, 1989) 83-93.
10. R. L. HUDSON and K. R. PARTHASARATHY, 'Quantum Ito's formula and stochastic evolutions', Comm. Math. Phys. 93 (1984) 301-323.
11. R. V. KADISON and J. R. RINGROSE, Fundamentals of the theory of operator algebras II: advanced theory, Graduate Studies in Mathematics 16 (American Mathematical Society, Providence, RI, 1997).
12. R. LENCZEWSKI, 'Filtered stochastic calculus', Infin. Dimens. Anal. Quantum Probab. Relat. Top. 4 (2001) 309-346.
13. J. M. LINDSAY, 'Quantum stochastic analysis -an introduction', Quantum independent increment processes I (eds M. Schürmann and U. Franz), Lecture Notes in Mathematics 1865 (Springer, Berlin, 2005) 181-271.
14. S. PATHMANATHAN, 'The Poisson process in quantum stochastic calculus', DPhil Thesis, University of Oxford, 2002.
15. M. REED and B. SIMON, Methods of modern mathematical physics I: functional analysis (Academic Press, New York, 1972).
16. M. REED and B. SIMON, Methods of modern mathematical physics II: Fourier analysis, self-adjointness (Academic Press, New York, 1975).
17. M. REED and B. SIMON, Methods of modern mathematical physics IV: analysis of operators (Academic Press, New York, 1978).
18. W. RUDIN, Real and complex analysis, 3rd edn (McGraw-Hill, New York, 1987).
19. W. RUDIN, Functional analysis, 2nd edn (McGraw-Hill, New York, 1991).
20. G. F. VINCENT-SMITH, 'The Itô formula for quantum semimartingales', Proc. London Math. Soc. (3) 75 (1997) 671-720.
21. G. F. VINCENT-SMITH, 'The Itô formula for perturbed Brownian martingales', Bull. London Math. Soc. 32 (2000) 736-745.
22. K. YOSIDA, Functional analysis, 6th edn (Springer, Berlin, 1980).