Splitting the conservation process into creation and annihilation parts

Nicolas Privault

Banach Center Publications (1998)

  • Volume: 43, Issue: 1, page 341-348
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Privault, Nicolas. "Splitting the conservation process into creation and annihilation parts." Banach Center Publications 43.1 (1998): 341-348. <http://eudml.org/doc/208855>.

@article{Privault1998,
abstract = {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.},
author = {Privault, Nicolas},
journal = {Banach Center Publications},
keywords = {Fock space; quantum stochastic calculus},
language = {eng},
number = {1},
pages = {341-348},
title = {Splitting the conservation process into creation and annihilation parts},
url = {http://eudml.org/doc/208855},
volume = {43},
year = {1998},
}

TY - JOUR
AU - Privault, Nicolas
TI - Splitting the conservation process into creation and annihilation parts
JO - Banach Center Publications
PY - 1998
VL - 43
IS - 1
SP - 341
EP - 348
AB - 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.
LA - eng
KW - Fock space; quantum stochastic calculus
UR - http://eudml.org/doc/208855
ER -

References

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  1. [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. 
  2. [2] J. M. C. Clark, The representation of functionals of Brownian motion by stochastic integrals, Ann. Math. Stat. 41 (1970), 1281-1295. 
  3. [3] R. L. Hudson and K. R. Parthasarathy, Quantum Itô's formula and stochastic evolutions, Commun. Math. Phys. 93 (1984), 301-323. Zbl0546.60058
  4. [4] J. M. Lindsay, Quantum and non-causal stochastic calculus, Probab. Theory Related Fields 97 (1993), 65-80. Zbl0794.60052
  5. [5] P. A. Meyer, Quantum Probability for Probabilists, volume 1538 of Lecture Notes in Mathematics, Springer-Verlag, Berlin/New York 1993. Zbl0773.60098
  6. [6] D. Nualart, The Malliavin Calculus and Related Topics, Probability and its Applications, Springer-Verlag, Berlin/New York 1995. Zbl0837.60050
  7. [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. Zbl0701.60048
  8. [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. 
  9. [9] N. Privault, A calculus on Fock space and its probabilistic interpretations, Bull. Sci. Math., to appear. 
  10. [10] N. Privault, An extension of the quantum Itô table and its matrix representation, to appear in Quantum Probability Communications X, World Scientific, 1998. 
  11. [11] D. Surgailis, On multiple Poisson stochastic integrals and associated Markov semi-groups, Probab. Math. Stat. 3 (1984), 217-239. Zbl0548.60058
  12. [12] A. S. Üstünel, Representation of the distributions on Wiener space and stochastic calculus of variations, J. Funct. Anal. 70 (1987), 126-129. 

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