Download PDF - Splitting the conservation process into creation and annihilation partsAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Splitting the conservation process into creation and annihilation parts

Authors 1

Affiliations

  1. Equipe d'Analyse et Probabilités, Université d'Evry-Val d'Essonne, Boulevard des Coquibus, 91025 Evry Cedex, France

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.

Bibliography

  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. J. M. C. Clark, The representation of functionals of Brownian motion by stochastic integrals, Ann. Math. Stat. 41 (1970), 1281-1295.
  3. R. L. Hudson and K. R. Parthasarathy, Quantum Itô's formula and stochastic evolutions, Commun. Math. Phys. 93 (1984), 301-323.
  4. J. M. Lindsay, Quantum and non-causal stochastic calculus, Probab. Theory Related Fields 97 (1993), 65-80.
  5. P. A. Meyer, Quantum Probability for Probabilists, volume 1538 of Lecture Notes in Mathematics, Springer-Verlag, Berlin/New York 1993.
  6. D. Nualart, The Malliavin Calculus and Related Topics, Probability and its Applications, Springer-Verlag, Berlin/New York 1995.
  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.
  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. N. Privault, A calculus on Fock space and its probabilistic interpretations, Bull. Sci. Math., to appear.
  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. D. Surgailis, On multiple Poisson stochastic integrals and associated Markov semi-groups, Probab. Math. Stat. 3 (1984), 217-239.
  12. A. S. Üstünel, Representation of the distributions on Wiener space and stochastic calculus of variations, J. Funct. Anal. 70 (1987), 126-129.
Banach Center Publications
1998/43/1
Export to PBN, Opens in new tab
Pages:
341-348
Main language of publication
English
Published
1998
Exact and natural sciences