# Quantum stochastic calculus on full Fock space

Banach Center Publications (1998)

- Volume: 43, Issue: 1, page 369-379
- ISSN: 0137-6934

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topSkeide, Michael. "Quantum stochastic calculus on full Fock space." Banach Center Publications 43.1 (1998): 369-379. <http://eudml.org/doc/208858>.

@article{Skeide1998,

abstract = {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.},

author = {Skeide, Michael},

journal = {Banach Center Publications},

keywords = {integration of time-adapted processes; creation; annihilating; conservation; Fock space; -algebra},

language = {eng},

number = {1},

pages = {369-379},

title = {Quantum stochastic calculus on full Fock space},

url = {http://eudml.org/doc/208858},

volume = {43},

year = {1998},

}

TY - JOUR

AU - Skeide, Michael

TI - Quantum stochastic calculus on full Fock space

JO - Banach Center Publications

PY - 1998

VL - 43

IS - 1

SP - 369

EP - 379

AB - 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.

LA - eng

KW - integration of time-adapted processes; creation; annihilating; conservation; Fock space; -algebra

UR - http://eudml.org/doc/208858

ER -

## References

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- [2] L. Accardi and Y. G. Lu, The Wigner semi-circle law in quantum electro dynamics, Commun. Math. Phys. 180 (1996), 605-632. Zbl0856.46047
- [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 Zbl0953.60527
- [4] R. L. Hudson and K. R. Parthasarathy, Quantum Ito's formula and stochastic evolutions, Commun. Math. Phys. 93 (1984), 301-323. Zbl0546.60058
- [5] B. Kümmerer and R. Speicher, Stochastic integration on the Cuntz algebra ${O}_{\infty}$, J. Funct. Anal. 103 (1992), 372-408. Zbl0787.46052
- [6] M. Skeide, Hilbert modules in quantum electro dynamics and quantum probability, Commun. Math. Phys. 192 (1998), 569-604. Zbl0928.46063
- [7] M. Skeide, Quantum stochastic calculus on full Fock modules, Preprint, Cottbus, 1998, in preparation.
- [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. Zbl0728.60060

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