The Azéma martingales as components of quantum independent increment processes

Michael Schürmann

Séminaire de probabilités de Strasbourg (1991)

  • Volume: 25, page 24-30

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Schürmann, Michael. "The Azéma martingales as components of quantum independent increment processes." Séminaire de probabilités de Strasbourg 25 (1991): 24-30. <http://eudml.org/doc/113760>.

@article{Schürmann1991,
author = {Schürmann, Michael},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {non-commutative stochastic processes; Hopf algebras; quantum stochastic calculus},
language = {fre},
pages = {24-30},
publisher = {Springer - Lecture Notes in Mathematics},
title = {The Azéma martingales as components of quantum independent increment processes},
url = {http://eudml.org/doc/113760},
volume = {25},
year = {1991},
}

TY - JOUR
AU - Schürmann, Michael
TI - The Azéma martingales as components of quantum independent increment processes
JO - Séminaire de probabilités de Strasbourg
PY - 1991
PB - Springer - Lecture Notes in Mathematics
VL - 25
SP - 24
EP - 30
LA - fre
KW - non-commutative stochastic processes; Hopf algebras; quantum stochastic calculus
UR - http://eudml.org/doc/113760
ER -

References

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  1. [1] Accardi, L., Frigerio, A., Lewis, J.T.: Quantum stochastic processes. Publ. RIMS, Kyoto Univ.18, 97-133 (1982) Zbl0498.60099MR660823
  2. [2] Accardi, L., Schürmann, M., Waldenfels, W. v. : Quantum independent increment processes on superalgebras. Math. Z.198, 451-477 (1988) Zbl0627.60014MR950578
  3. [3] Azéma, J.: Sur les fermes aleatoires. In: Azema, J., Yor, M. (eds.) Sem. Prob.XIX. (Lect. Notes Math., vol. 1123). BerlinHeidelbergNew York: Springer1985 Zbl0563.60038MR889496
  4. [4] Glockner, P.: *-Bialgebren in der Quantenstochastik. Dissertation, Heidelberg1989 Zbl0688.60005
  5. [5] Glockner, P., Waldenfels, W. v. : The relations of the non-commutative coefficient algebra of the unitary group. SFB-Preprint Nr. 460, Heidelberg1988 
  6. [6] Guichardet, A.: Symmetric Hilbert spaces and related topics. (Lect. Notes Math. vol. 261). BerlinHeidelbergNew York : Springer1972 Zbl0265.43008MR493402
  7. [7] Parthasarathy, K.R.: Azema martingales and quantum stochastic calculus. Preprint 1989 
  8. [8] Parthasarathy, K.R., Schmidt, K.: Positive definite kernels, continuous tensor products, and central limit theorems of probability theory. (Lect. Notes Math. vol. 272). BerlinHeidelbergNew York : Springer1972 Zbl0237.43005MR622034
  9. [9] Schürmann, M.: Noncommutative stochastic processes with independent and stationary increments satisfy quantum stochastic differential equations. To appear in Probab. Th. Rel. Fields Zbl0668.60058MR1042061
  10. [10] Schürmann, M.: A class of representations of involutive bialgebras. To appear in Math. Proc. Cambridge Philos. Soc. Zbl0704.46040MR1021880
  11. [11] Schürmann, M.: Quantum stochastic processes with independent additive increments. Preprint, Heidelberg1989 MR1128934
  12. [12] Sweedler, M.E.: Hopf algebras. New York : Benjamin1969 Zbl0194.32901MR252485

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