Filtered stochastic calculus

Infinite Dimensional Analysis, Quantum Probability and Related Topics

Volumn 4, Issue 3, 2001, Pages 309-346

  Lenczewski, Romuald ^a  

^a WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035627338     PISSN: 02190257     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219025701000553     Document Type: Article

References (28)

1. L. Accardi, F. Fagnola and J. Quacgebeur, A representation free quantum stochastic calculus, J. Funct. Anal. 104 (1992) 149-197.
2. S. Attal and M. Lindsay, Quantum stochastic calculus - a maximal formulation, Preprint No. 456 (1999), CNRS, Univ. de Grenoble I.
3. D. B. Applebaum and R. H. Hudson, Fermion Itô's formula and stochastic evolutions, Comm. Math. Phys. 96 (1984) 437-496.
4. A. Boukas, Quantum stochastic analysis: A non-Brownian case, Ph.D. Thesis, Southern Illinois University (1988).
5. C. Barnett, R. F. Streater and I. F. Wilde, Quasi-free quantum stochastic integrals for the CAR and CCR, J. Funct. Anal. 52 (1983) 19-47.
6. A. Belton, Quantum Ω-semimartingales and stochastic evolutions, preprint (2000).
7. V. P. Belavkin, Chaotic states and stochastic integration in quantum systems, Usp. Mat. Nauk 47 (1992) 47-106.
8. P. Biane and R. Speicher, Stochastic calculus with respect to free Brownian motion and analysis on Wigner space, preprint.
9. F. Fagnola, On quantum stochastic integration with respect to free noises, in Quantum Probability and Related Topics, World Scientific, London (1991).
10. U. Franz and R. Lenczewski, Limit theorems for the hierarchy of freeness, Prob. Math. Stat. 19 (1999) 23-41.
11. U. Franz, R. Lenczewski and M. Schürmann, The GNS construction for the hierarchy of freeness, Preprint No. 9/98, Wroclaw University of Technology (1998).
12. R. L. Hudson and K. R. Parthasarathy, Quantum Itô's formula and stochastic evolutions, Comm. Math. Phys. 93 (1984) 301-323.
13. R. L. Hudson and K. R. Parthasarathy, Unification of fermion and boson stochastic calculus, Comm. Math. Phys. 104 (1986) 457-470.
14. ∞, J. Funct. Anal. 103 (1992) 372-408.
15. R. Lenczewski, Unification of independence in quantum probability, Infinite Dimensional Anal. Quantum Probab. Related Topics 1 (1998) 383-405.
16. R. Lenczewski, Filtered probability I: Random variables, limit theorems and fundamental operators, Preprint No. 16 (1999), Wroclaw University of Technology.
17. M. Lindsay, Quantum and non-causal stochastic calculus, Probab. Th. Rel. Fields 97 (1993) 65-80.
18. H. Maassen, Quantum Markov processes on Fock space described by integral kernels, in Quantum Probability and Applications II, Lecture Notes in Math., Vol. 1136, eds. L. Accardi and W. V. Waldenfels (Springer, 1985).
19. P. A. Meyer, Quantum Probability for Probabilists, Lecture Notes in Math., Vol. 1538 (Springer-Verlag, 1993).
20. A. Mohari and K. B. Sinha, Quantum stochastic flows with infinite degrees of freedom and countable state Markov processes, Sankhya, Ser. A, Part I (1990), pp. 43-57.
21. K. R. Parthasarathy, An Introduction to Quantum Stochastic Calculus (Birkhäuser, 1992).
22. K. R. Parthasarathy and K. B. Sinha, Unification of quantum noise processes in Fock spaces, in Proc. Trento Conference on Quantum Probability and Applications (1989).
23. M. Schürmann, White Noise on Bialgebras, Lecture Notes in Math., Vol. 1544 (Springer, 1991).
24. M. Schürmann, Direct sums of tensor products and non-commutative independence, J. Funct. Anal. 133 (1995) 1-9.
25. R. Speicher, On universal products, Fields Institute Comm. 12 (1997) 257-266.
26. R. Speicher, Stochastic integration on the full Fock space with the help of a kernel calculus, Publ. R.I.M.S. Kyoto Univ. 27 (1991) 149-184.
27. G. F. Vincent-Smith, Classical and quantum dynamical propagators, Oxford, preprint (1990).
28. D. Voiculescu, Symmetries of some reduced free product C*-algebras, in Operator Algebras and their Connections with Topology and Ergodic Theory, Lecture Notes in Math., Vol. 1132 (Springer, 1985), pp. 556-588.