The aim of this paper is the study of a non-commutative decomposition of the conservation process in quantum stochastic calculus. The probabilistic interpretation of this decomposition uses time changes, in contrast to the spatial shifts used in the interpretation of the creation and annihilation operators on Fock space.
@article{bwmeta1.element.bwnjournal-article-bcpv43i1p341bwm, author = {Privault, Nicolas}, title = {Splitting the conservation process into creation and annihilation parts}, journal = {Banach Center Publications}, volume = {43}, year = {1998}, pages = {341-348}, zbl = {0948.60053}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv43i1p341bwm} }
Privault, Nicolas. Splitting the conservation process into creation and annihilation parts. Banach Center Publications, Tome 43 (1998) pp. 341-348. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv43i1p341bwm/
[000] [1] P. Biane, Calcul stochastique non-commutatif, in: Ecole d'été de Probabilités de Saint-Flour, volume 1608 of Lecture Notes in Mathematics, Saint-Flour, 1993. Springer-Verlag.
[001] [2] J. M. C. Clark, The representation of functionals of Brownian motion by stochastic integrals, Ann. Math. Stat. 41 (1970), 1281-1295.
[002] [3] R. L. Hudson and K. R. Parthasarathy, Quantum Itô's formula and stochastic evolutions, Commun. Math. Phys. 93 (1984), 301-323. | Zbl 0546.60058
[003] [4] J. M. Lindsay, Quantum and non-causal stochastic calculus, Probab. Theory Related Fields 97 (1993), 65-80. | Zbl 0794.60052
[004] [5] P. A. Meyer, Quantum Probability for Probabilists, volume 1538 of Lecture Notes in Mathematics, Springer-Verlag, Berlin/New York 1993. | Zbl 0773.60098
[005] [6] D. Nualart, The Malliavin Calculus and Related Topics, Probability and its Applications, Springer-Verlag, Berlin/New York 1995. | Zbl 0837.60050
[006] [7] D. Nualart and J. Vives, Anticipative calculus for the Poisson process based on the Fock space, in: J. Azéma, P.A. Meyer, and M. Yor (eds.), Séminaire de Probabilités XXIV, volume 1426 of Lecture Notes in Mathematics, pp. 154-165. Springer-Verlag, Berlin/New York 1990. | Zbl 0701.60048
[007] [8] D. Ocone, A guide to the stochastic calculus of variations, in: H. Körezlioǧlu and A.S. Üstünel (eds.), Stochastic Analysis and Related Topics, Silivri, 1988; volume 1316 of Lecture Notes in Mathematics, Springer-Verlag, Berlin/New York 1988.
[008] [9] N. Privault, A calculus on Fock space and its probabilistic interpretations, Bull. Sci. Math., to appear.
[009] [10] N. Privault, An extension of the quantum Itô table and its matrix representation, to appear in Quantum Probability Communications X, World Scientific, 1998.
[010] [11] D. Surgailis, On multiple Poisson stochastic integrals and associated Markov semi-groups, Probab. Math. Stat. 3 (1984), 217-239. | Zbl 0548.60058
[011] [12] A. S. Üstünel, Representation of the distributions on Wiener space and stochastic calculus of variations, J. Funct. Anal. 70 (1987), 126-129.