@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},
volume = {6},
year = {1999},
pages = {41-61},
mrnumber = {1735278},
zbl = {01416127},
language = {en},
url = {http://dml.mathdoc.fr/item/AMBP_1999__6_2_41_0}
}
Privault, Nicolas; Wu, Jiang-Lun. Poisson stochastic integration in Hilbert spaces. Annales mathématiques Blaise Pascal, Tome 6 (1999) pp. 41-61. http://gdmltest.u-ga.fr/item/AMBP_1999__6_2_41_0/
[1] and . Non adapted stochastic calculus as third quantization. Random Operators and Stochastic Equations, 4(1):77-89, 1996. | Zbl 0849.60098
[2] . Spectral families of quantum stochastic integrals. Communications in Mathematical Physics, 170:607-628, 1995. | MR 1337135 | Zbl 0851.60068
[3] and . Infinite series of quantum spectral stochastic integrals. Journal of Operator Theory, 36:295-316, 1996. | MR 1432120 | Zbl 0868.46046
[4] . Classical and quantum stochastic calculus. In Quantum Probability Communications, volume X, pages 1-52. World Scientific, Singapore, 1998. | MR 1689473
[5] . A Quantum Nonadapted Ito Formula and Stochastic Analysis in Fock Scale. J. Funct. Anal., 102:414-447, 1991. | MR 1140634 | Zbl 0737.60042
[6] , , and . 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 960543 | Zbl 0653.60045
[7] . Symmetric Hilbert spaces and related topics, volume 261 of Lecture Notes in Mathematics. Springer Verlag, 1970. | MR 493402 | Zbl 0265.43008
[8] . Introduction to the theory of Hilbert spaces and spectral multiplicity. 2nd ed.Chelsea Publishing Company, New York, 1957. | Zbl 0079.12404
[9] . Stochastic integrals on general topological measurable spaces. Zeitschrift für Wahrscheinlichkeitstheories verw. Gebiete, 66:25-40, 1984. | MR 743083 | Zbl 0519.60054
[10] and . Quantum Itô's formula and stochastic evolutions. Communications in Mathematical Physics, 93:301-323, 1984. | MR 745686 | Zbl 0546.60058
[11] . Generalized Poisson functionals. Probab. Theory Related Fields, 77:1-28, 1988. | MR 921816 | Zbl 0617.60035
[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 0794.60052
[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 474493 | Zbl 0439.60044
[15] and . 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 1360277 | Zbl 0856.60057
[16] . An Introduction to Quantum Stochastic Calculus. Birkäuser, 1992. | Zbl 0751.60046
[17] . Formules de dualité sur l'espace de Poisson. Ann. Inst. H. Poincaré Probab. Statist., 32(4):509-548, 1996. | Numdam | MR 1411270 | Zbl 0859.60045
[18] . On multiple Poisson stochastic integrals and associated Markov semi-groups. Probability and Mathematical Statistics, 3:217-239, 1984. | MR 764148 | Zbl 0548.60058
[19] . Construction du calcul stochastique sur un espace de Wiener abstrait. C. R. Acad. Sci. Paris Sér. I Math., 305:279-282, 1987. | MR 907962 | Zbl 0637.60068
[20] and . The construction of filtrations on abstract Wiener space. J. Funct. Anal., 143(1):10-32, 1997. | MR 1428114 | Zbl 0873.60039
[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 1071539 | Zbl 0723.60064