Erratum: An isomorphism of quantum semimartingale algebras (Quarterly Journal Mathematics (2004) 55 (135-165) DOI: 10.1093/qmath/hag052);An isomorphism of quantum semimartingale algebras

Quarterly Journal of Mathematics

Volumn 55, Issue 2, 2004, Pages 135-165

  Belton, Alexander C R ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

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[No Author keywords available]

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EID: 4043144966     PISSN: 00335606     EISSN: None     Source Type: Journal    
DOI: 10.1093/qmath/hah999     Document Type: Erratum

References (24)

1. S. Attal, An algebra of non-commutative bounded semimartingales: square and angle quantum brackets, J. Funct. Anal. 124 (1994), 292-332.
2. S. Attal, Extensions of Quantum Stochastic Calculus, Prépublications de l'Institut Fourier 455, Grenoble, 1999. 〈http://www-fourier.ujf-grenoble.fr/PREP/prep_if.html〉
3. S. Attal, The structure of the quantum semimartingale algebras, J. Operator Theory 46 (2001), 391-410.
4. S. Attal and J. M. Lindsay, Quantum stochastic calculus with maximal operator domains, Ann. Probab. to appear.
5. S. Attal and P.-A. Meyer, Interprétation probabiliste et extension des intégrales stochastiques non commutatives, Séminaire de Probabilités XXVII, Lecture Notes in Mathematics, 1557, (Eds J. Azéma, P.-A. Meyer, and M. Yor), Springer, Berlin, 1993, 312-327.
6. J. Azéma, Sur les fermés aléatoires, Séminaire de Probabilités XIX, Lecture Notes in Mathematics, 1123, (Eds J. Azéma and M. Yor), Springer, Berlin, 1985, 397-495.
7. V. P. Belavkin, A quantum non-adapted Ito formula and stochastic analysis in Fock scale, J. Funct. Anal. 102 (1991), 414-447.
8. A. C. R. Belton, Quantum Ω-semimartingales and stochastic evolutions, J. Funct. Anal 187 (2001), 94-109.
9. F. Fagnola, Characterization of isometric and unitary weakly differentiable cocycles in Fock space, Quantum Probability and Related Topics VIII, (Ed. L. Accardi), World Scientific, London, 1993, 143-164.
10. R. L. Hudson and P. Krée, Quantum stochastic calculus for Hilbert-Schmidt processes Stochastic Analysis, Path Integration and Dynamics, Warwick 1987, Pitman Research Notes in Mathematics Series 200, (Eds K. D. Elworthy and J.-C. Zambrini), Longman Scientific & Technical, Harlow, 1989, 83-93.
11. R. L. Hudson and K. R. Parthasarathy, Quantum Ito's formula and stochastic evolutions, Comm. Math. Phys. 93 (1984), 301-323.
12. R. L. Hudson, J. M. Lindsay, and K. R. Parthasarathy, Stochastic integral representation of some quantum martingales in Fock space, From Local Times to Global Geometry, Control and Physics, Pitman Research Notes in Mathematics Series 150, (Ed. K. D. Elworthy), Longman Scientific & Technical, Harlow, 1986, 121-131.
13. J. M. Lindsay, Quantum and non-causal stochastic calculus, Probab. Theory Relat. Fields 97 (1993), 65-80.
14. J. M. Lindsay, Totality for convenient families of exponential vectors, private communication, 2000.
15. P.-A. Meyer, Quantum Probability for Probabilists, 2nd edn, Lecture Notes in Mathematics 1538, Springer, Berlin, 1995.
16. K. R. Parthasarathy, Azéma martingales and quantum stochastic calculus, Proceedings of the R. C. Bose Symposium on Probability, Statistics and Design of Experiments, (Ed. R. R. Bahadur), Wiley Eastern, New Delhi, 1990, 551-569.
17. K. R. Parthasarathy and K. B. Sinha, Stochastic integral representation of bounded quantum martingales in Fock space, J. Funct. Anal. 67 (1986), 126-151.
18. K. R. Parthasarathy and K. B. Sinha, Representation of a class of quantum martingales II, Quantum Probability and Applications III, Lecture Notes in Mathematics 1303, (Eds L. Accardi and W. von Waldenfels), Springer, Berlin, 1988, 232-250.
19. 2[0,1]), Quantum Probability Communications X, (Eds R. L. Hudson and J. M. Lindsay), World Scientific, London, 1998, 281-284.
20. P. Protter, Stochastic Integration and Differential Equations, a New Approach, Applications of Mathematics 21, Springer, Berlin, 1990.
21. L. C. G. Rogers and D. Williams, Diffusions, Markov Processes and Martingales. Volume II: Itô calculus, 2nd edn, Cambridge University Press, Cambridge, 2000.
22. W. Rudin, Functional Analysis, 2nd edn, McGraw-Hill, London, 1991.
23. +)), Trends in Contemporary Infinite Dimensional Analysis and Quantum Probability, Volume in honour of Takeyuki Hida, (Eds L. Accardi, H. H. Kuo, N. Obata, K. Saito, Si Si, and L. Streit), Istituto Italiano di Cultura (ISEAS), Kyoto, 2000.
24. K. Yosida, Functional Analysis, 6th edn, Grundlehren der Mathematischen Wissenschaften 123, Springer, Berlin, 1980.