Poisson stochastic integration in Hilbert spaces
Annales mathématiques Blaise Pascal, Tome 6 (1999) no. 2, pp. 41-61. 
@article{AMBP_1999__6_2_41_0,
     author = {Privault, Nicolas and Wu, Jiang-Lun},
     title = {Poisson stochastic integration in {Hilbert} spaces},
     journal = {Annales math\'ematiques Blaise Pascal},
     pages = {41--61},
     publisher = {Laboratoires de Math\'ematiques Pures et Appliqu\'ees de l'Universit\'e Blaise Pascal},
     volume = {6},
     number = {2},
     year = {1999},
     mrnumber = {1735278},
     zbl = {01416127},
     language = {en},
     url = {http://archive.numdam.org/item/AMBP_1999__6_2_41_0/}
}
TY  - JOUR
AU  - Privault, Nicolas
AU  - Wu, Jiang-Lun
TI  - Poisson stochastic integration in Hilbert spaces
JO  - Annales mathématiques Blaise Pascal
PY  - 1999
SP  - 41
EP  - 61
VL  - 6
IS  - 2
PB  - Laboratoires de Mathématiques Pures et Appliquées de l'Université Blaise Pascal
UR  - http://archive.numdam.org/item/AMBP_1999__6_2_41_0/
LA  - en
ID  - AMBP_1999__6_2_41_0
ER  - 
%0 Journal Article
%A Privault, Nicolas
%A Wu, Jiang-Lun
%T Poisson stochastic integration in Hilbert spaces
%J Annales mathématiques Blaise Pascal
%D 1999
%P 41-61
%V 6
%N 2
%I Laboratoires de Mathématiques Pures et Appliquées de l'Université Blaise Pascal
%U http://archive.numdam.org/item/AMBP_1999__6_2_41_0/
%G en
%F AMBP_1999__6_2_41_0
Privault, Nicolas; Wu, Jiang-Lun. Poisson stochastic integration in Hilbert spaces. Annales mathématiques Blaise Pascal, Tome 6 (1999) no. 2, pp. 41-61. http://archive.numdam.org/item/AMBP_1999__6_2_41_0/

[1] L. Accardi and I. Pikovski. Non adapted stochastic calculus as third quantization. Random Operators and Stochastic Equations, 4(1):77-89, 1996. | Zbl

[2] D. Applebaum. Spectral families of quantum stochastic integrals. Communications in Mathematical Physics, 170:607-628, 1995. | MR | Zbl

[3] D. Applebaum and M. Brooks. Infinite series of quantum spectral stochastic integrals. Journal of Operator Theory, 36:295-316, 1996. | MR | Zbl

[4] S. Attal. Classical and quantum stochastic calculus. In Quantum Probability Communications, volume X, pages 1-52. World Scientific, Singapore, 1998. | MR

[5] V.P. Belavkin. A Quantum Nonadapted Ito Formula and Stochastic Analysis in Fock Scale. J. Funct. Anal., 102:414-447, 1991. | MR | Zbl

[6] A. Dermoune, P. Krée, and L. Wu. Calcul stochastique non adapté par rapport à la mesure de Poisson. In Séminaire de Probabilités XXII, volume 1321 of Lecture Notes in Mathematics. Springer Verlag, 1988. | Numdam | MR | Zbl

[7] A. Guichardet. Symmetric Hilbert spaces and related topics, volume 261 of Lecture Notes in Mathematics. Springer Verlag, 1970. | MR | Zbl

[8] P.R. Halmos. Introduction to the theory of Hilbert spaces and spectral multiplicity. 2nd ed.Chelsea Publishing Company, New York, 1957. | Zbl

[9] Z.Y. Huang. Stochastic integrals on general topological measurable spaces. Zeitschrift für Wahrscheinlichkeitstheories verw. Gebiete, 66:25-40, 1984. | MR | Zbl

[10] R.L. Hudson and K.R. Parthasarathy. Quantum Itô's formula and stochastic evolutions. Communications in Mathematical Physics, 93:301-323, 1984. | MR | Zbl

[11] Y. Ito. Generalized Poisson functionals. Probab. Theory Related Fields, 77:1-28, 1988. | MR | Zbl

[12] V. Liebscher. On the isomorphism of Poisson space and Fock space. In Quantum Probability and Related Topics, volume IX, pages 295-300, Singapore, 1994. World Scientific.

[13] J.M. Lindsay. Quantum and non-causal stochastic calculus. Probab. Theory Related Fields, 97:65-80, 1993. | Zbl

[14] J. Neveu. Processus ponctuels. In Ecole d'été de Probabilités de Saint-Flour VI, volume 598 of Lecture Notes in Mathematics, pages 249-445. Springer-Verlag, 1977. | MR | Zbl

[15] D. Nualart and J. Vives. A duality formula on the Poisson space and some applications. In E. Bolthausen, M. Dozzi, and F. Russo, Seminar on Stochastic Analysis, Random Fields and Applications, Progress in Probability, pages 205-213, Ascona, 1993. Birkäuser. | MR | Zbl

[16] K.R. Parthasarathy. An Introduction to Quantum Stochastic Calculus. Birkäuser, 1992. | Zbl

[17] J. Picard. Formules de dualité sur l'espace de Poisson. Ann. Inst. H. Poincaré Probab. Statist., 32(4):509-548, 1996. | Numdam | MR | Zbl

[18] D. Surgailis. On multiple Poisson stochastic integrals and associated Markov semi-groups. Probability and Mathematical Statistics, 3:217-239, 1984. | MR | Zbl

[19] A.S. Üstünel. Construction du calcul stochastique sur un espace de Wiener abstrait. C. R. Acad. Sci. Paris Sér. I Math., 305:279-282, 1987. | MR | Zbl

[20] A.S. Üstünel and M. Zakai. The construction of filtrations on abstract Wiener space. J. Funct. Anal., 143(1):10-32, 1997. | MR | Zbl

[21] L. Wu. Un traitement unifié de la représentation des fonctionnelles de Wiener. In Séminaire de Probabilités, XXIV, 1988/89, volume 1426 of Lecture Notes in Mathematics, pages 166-187. Springer-Verlag, 1990. | Numdam | MR | Zbl