Quantum stochastic calculus on full Fock space
Skeide, Michael
Banach Center Publications, Tome 43 (1998), p. 369-379 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

We present a new version of integration of time-adapted processes with respect to creation, annihilation and conservation processes on the full Fock space. Among the new features, in the first place, there is a new formulation of adaptedness which is both simpler and more general than the known ones. The new adaptedness allows for processes which are not restricted to be elements of some norm closure of the ∗-algebra which is generated by the basic creation processes.

Publié le : 1998-01-01
EUDML-ID : urn:eudml:doc:208858 
@article{bwmeta1.element.bwnjournal-article-bcpv43i1p369bwm,
     author = {Skeide, Michael},
     title = {Quantum stochastic calculus on full Fock space},
     journal = {Banach Center Publications},
     volume = {43},
     year = {1998},
     pages = {369-379},
     zbl = {0978.46040},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv43i1p369bwm}
}

Skeide, Michael. Quantum stochastic calculus on full Fock space. Banach Center Publications, Tome 43 (1998) pp. 369-379. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv43i1p369bwm/

[000] [1] L. Accardi, F. Fagnola and J. Quaegebeur, A representation free quantum stochastic calculus, J. Funct. Anal. 104 (1992), 149-197. | Zbl 0759.60068

[001] [2] L. Accardi and Y. G. Lu, The Wigner semi-circle law in quantum electro dynamics, Commun. Math. Phys. 180 (1996), 605-632. | Zbl 0856.46047

[002] [3] F. Fagnola, On quantum stochastic integration with respect to 'free' noises, Accardi, L. (ed.), Quantum Probability & Related Topics VI, Singapore, New Jersey, London, Hong Kong, World Scientific, 1991 | Zbl 0953.60527

[003] [4] R. L. Hudson and K. R. Parthasarathy, Quantum Ito's formula and stochastic evolutions, Commun. Math. Phys. 93 (1984), 301-323. | Zbl 0546.60058

[004] [5] B. Kümmerer and R. Speicher, Stochastic integration on the Cuntz algebra O∞, J. Funct. Anal. 103 (1992), 372-408. | Zbl 0787.46052

[005] [6] M. Skeide, Hilbert modules in quantum electro dynamics and quantum probability, Commun. Math. Phys. 192 (1998), 569-604. | Zbl 0928.46063

[006] [7] M. Skeide, Quantum stochastic calculus on full Fock modules, Preprint, Cottbus, 1998, in preparation.

[007] [8] R. Speicher, Stochastic integration on the full Fock space with the help of a kernel calculus, Publ. RIMS Kyoto Univ. 27 (1991), 149-184. | Zbl 0728.60060