@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] Non adapted stochastic calculus as third quantization. Random Operators and Stochastic Equations, 4(1):77-89, 1996. | Zbl
and .[2] Spectral families of quantum stochastic integrals. Communications in Mathematical Physics, 170:607-628, 1995. | MR | Zbl
.[3] Infinite series of quantum spectral stochastic integrals. Journal of Operator Theory, 36:295-316, 1996. | MR | Zbl
and .[4] Classical and quantum stochastic calculus. In Quantum Probability Communications, volume X, pages 1-52. World Scientific, Singapore, 1998. | MR
.[5] A Quantum Nonadapted Ito Formula and Stochastic Analysis in Fock Scale. J. Funct. Anal., 102:414-447, 1991. | MR | Zbl
.[6] 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
, , and .[7] Symmetric Hilbert spaces and related topics, volume 261 of Lecture Notes in Mathematics. Springer Verlag, 1970. | MR | Zbl
.[8] Introduction to the theory of Hilbert spaces and spectral multiplicity. 2nd ed.Chelsea Publishing Company, New York, 1957. | Zbl
.[9] Stochastic integrals on general topological measurable spaces. Zeitschrift für Wahrscheinlichkeitstheories verw. Gebiete, 66:25-40, 1984. | MR | Zbl
.[10] Quantum Itô's formula and stochastic evolutions. Communications in Mathematical Physics, 93:301-323, 1984. | MR | Zbl
and .[11] Generalized Poisson functionals. Probab. Theory Related Fields, 77:1-28, 1988. | MR | Zbl
.[12] 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] Quantum and non-causal stochastic calculus. Probab. Theory Related Fields, 97:65-80, 1993. | Zbl
.[14] 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] 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
and .[16] An Introduction to Quantum Stochastic Calculus. Birkäuser, 1992. | Zbl
.[17] Formules de dualité sur l'espace de Poisson. Ann. Inst. H. Poincaré Probab. Statist., 32(4):509-548, 1996. | Numdam | MR | Zbl
.[18] On multiple Poisson stochastic integrals and associated Markov semi-groups. Probability and Mathematical Statistics, 3:217-239, 1984. | MR | Zbl
.[19] 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] The construction of filtrations on abstract Wiener space. J. Funct. Anal., 143(1):10-32, 1997. | MR | Zbl
and .[21] 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
.