@article{AIHPB_2005__41_3_581_0, author = {Lindsay, J. Martin and Skalski, Adam G.}, title = {Quantum stochastic convolution cocycles {I}}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {581--604}, publisher = {Elsevier}, volume = {41}, number = {3}, year = {2005}, doi = {10.1016/j.anihpb.2004.10.002}, mrnumber = {2139034}, zbl = {1074.81044}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpb.2004.10.002/} }
TY - JOUR AU - Lindsay, J. Martin AU - Skalski, Adam G. TI - Quantum stochastic convolution cocycles I JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2005 SP - 581 EP - 604 VL - 41 IS - 3 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpb.2004.10.002/ DO - 10.1016/j.anihpb.2004.10.002 LA - en ID - AIHPB_2005__41_3_581_0 ER -
%0 Journal Article %A Lindsay, J. Martin %A Skalski, Adam G. %T Quantum stochastic convolution cocycles I %J Annales de l'I.H.P. Probabilités et statistiques %D 2005 %P 581-604 %V 41 %N 3 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpb.2004.10.002/ %R 10.1016/j.anihpb.2004.10.002 %G en %F AIHPB_2005__41_3_581_0
Lindsay, J. Martin; Skalski, Adam G. Quantum stochastic convolution cocycles I. Annales de l'I.H.P. Probabilités et statistiques, Volume 41 (2005) no. 3, pp. 581-604. doi : 10.1016/j.anihpb.2004.10.002. http://archive.numdam.org/articles/10.1016/j.anihpb.2004.10.002/
[1] On the quantum Feynman-Kac formula, Rend. Sem. Mat. Fis. Milano 48 (1978) 135-180. | MR | Zbl
,[2] On multidimensional Markovian cocycles, in: , (Eds.), Quantum Probability and Applications IV, Lecture Notes in Math., vol. 1396, Springer-Verlag, Berlin, 1989, pp. 59-67. | MR | Zbl
, , ,[3] On the structure of classical and quantum flows, J. Funct. Anal. 135 (2) (1996) 421-455. | MR | Zbl
, ,[4] Noncommutative Dynamics and E-Semigroups, Springer-Verlag, New York, 2003. | MR | Zbl
,[5] Quantum independent increment processes on superalgebras, Math. Z. 198 (4) (1988) 451-477. | MR | Zbl
, , ,[6] Quantum Independent Increment Processes I: From Classical Probability to Quantum Stochastics, Lecture Notes in Math., vol. 1865, Springer-Verlag, Heidelberg, 2005. | MR | Zbl
, , , ,[7] O.E. Barndorff-Nielsen, U. Franz, G. Gohm, B. Krümmerer, S. Thorbjørsen, Quantum Independent Increment Processes II: Structure of Quantum Lévy Processes, Classical Probability and Physics, U. Franz, M. Schürmann (Eds.), Lecture Notes in Math., vol. 1866, Springer-Verlag, Heidelberg, in press. | MR
[8] Stochastic cocycles as a characterisation of quantum flows, Bull. Sci. Math. 116 (1) (1992) 1-34. | MR | Zbl
,[9] Perturbations of quantum diffusions, J. London Math. Soc. (2) 41 (2) (1990) 373-384. | MR | Zbl
, ,[10] Characterization of isometric and unitary weakly differentiable cocycles in Fock space, in: (Ed.), Quantum Probability and Related Topics VIII, World Scientific, Singapore, 1993, pp. 143-164. | MR
,[11] U. Franz, Lévy processes on quantum groups and dual groups, in [7]. | Zbl
[12] Stochastic Processes and Operator Calculus on Quantum Groups, Math. Appl., vol. 490, Kluwer Academic, Dordrecht, 1999. | MR | Zbl
, ,[13] Quantum stochastic differential equations on *-bialgebras, Math. Proc. Cambridge Philos. Soc. 109 (3) (1991) 571-595. | MR | Zbl
,[14] A stochastic Stinespring theorem, Math. Ann. 319 (4) (2001) 647-673. | MR | Zbl
, , ,[15] Symmetric Hilbert Spaces and Related Topics, Lecture Notes in Math., vol. 267, Springer, Heidelberg, 1970. | MR | Zbl
,[16] J. Hellmich, C. Köstler, B. Kümmerer, Noncommutative continuous Bernoulli shifts, Preprint, Queen's University, Kingston, 2004.
[17] Unitarity and multiplicativity via higher Itô product formula, Tatra Mt. Math. Publ. 10 (1997) 95-108. | MR | Zbl
,[18] On characterizing quantum stochastic evolutions, Math. Proc. Cambridge Philos. Soc. 102 (2) (1987) 363-369. | MR | Zbl
, ,[19] Quantum Itô's formula and stochastic evolutions, Comm. Math. Phys. 93 (3) (1984) 301-323. | MR | Zbl
, ,[20] Structure des cocycles markoviens sur l'espace de Fock, Probab. Theory Related Fields 75 (2) (1987) 291-316. | MR | Zbl
,[21] J. Kustermans, Locally compact quantum groups, in [6]. | Zbl
[22] Locally compact quantum groups, Ann. Sci. École Norm. Sup. (4) 33 (6) (2000) 837-934. | Numdam | MR | Zbl
, ,[23] Integral-sum kernel operators, in: , (Eds.), Quantum Probability Communications XII, World Scientific, Singapore, 2003, pp. 1-21. | MR | Zbl
,[24] J.M. Lindsay, Quantum stochastic analysis - an introduction, in [6]. | Zbl
[25] J.M. Lindsay, A.G. Skalski, Quantum stochastic convolution cocycles-algebraic and -algebraic, in: M. Bożejko, R. Lenczewski, W. Młotkowski, J. Wysoczański (Eds.), Quantum Probability and Related Topics, Banach Center Publications, Polish Academy of Sciences, Warsaw, 2005, in press. | Zbl
[26] Existence, positivity, and contractivity for quantum stochastic flows with infinite dimensional noise, Probab. Theory Related Fields 116 (4) (2000) 505-543. | MR | Zbl
, ,[27] Markovian cocycles on operator algebras, adapted to a Fock filtration, J. Funct. Anal. 178 (2) (2000) 269-305. | MR | Zbl
, ,[28] Homomorphic Feller cocycles on a -algebra, J. London Math. Soc. (2) 68 (1) (2003) 255-272. | Zbl
, ,[29] J.M. Lindsay, S.J. Wills, Operator Markovian cocycles via associated semigroups, Preprint, 2004.
[30] Quantum Markov processes on Fock space described by integral kernels, in: , (Eds.), Quantum Probability and Applications II, Lecture Notes in Math., vol. 1136, Springer-Verlag, Berlin, 1985, pp. 361-374. | MR
,[31] Quantum Probability for Probabilists, Lecture Notes in Math., vol. 1538, Springer-Verlag, Berlin, 1995. | MR | Zbl
,[32] Introduction to Quantum Stochastic Calculus, Birkhäuser, Basel, 1992. | MR | Zbl
,[33] Unbounded Operator Algebras and Representation Theory, Akademie-Verlag, Berlin, 1990. | MR | Zbl
,[34] Noncommutative stochastic processes with independent and stationary increments satisfy quantum stochastic differential equations, Probab. Theory Related Fields 84 (4) (1990) 473-490. | MR | Zbl
,[35] White noise on involutive bialgebras, in: Quantum Probability & Related Topics VI, World Scientific, Singapore, 1991, pp. 401-419. | MR | Zbl
,[36] White Noise on Bialgebras, Lecture Notes in Math., vol. 1544, Springer, Heidelberg, 1993. | MR | Zbl
,[37] Operator processes majorizing their quadratic variation, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 3 (1) (2000) 99-120. | MR | Zbl
,[38] Operator stochastic differential equations and stochastic semigroups, Uspekhi Mat. Nauk 37 (6) (1982) 157-183, (228) (in Russian), Russian Math. Surveys 37 (6) (1982) 177-204. | MR | Zbl
,[39] Hopf Algebras, Benjamin, New York, 1969. | MR | Zbl
,[40] Compact matrix pseudogroups, Comm. Math. Phys. 111 (4) (1987) 613-665. | MR | Zbl
,[41] Compact quantum groups, in: , , (Eds.), Symétries Quantiques, Proceedings, Les Houches, 1995, North-Holland, Amsterdam, 1998, pp. 845-884. | MR | Zbl
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