@article{AMBP_1999__6_2_41_0,
author = {Nicolas Privault and Jiang-Lun Wu},
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},
zbl = {01416127},
mrnumber = {1735278},
language = {en},
url = {https://ambp.centre-mersenne.org/item/AMBP_1999__6_2_41_0/}
}
TY - JOUR AU - Nicolas Privault AU - Jiang-Lun Wu 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 - https://ambp.centre-mersenne.org/item/AMBP_1999__6_2_41_0/ LA - en ID - AMBP_1999__6_2_41_0 ER -
%0 Journal Article %A Nicolas Privault %A Jiang-Lun Wu %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 https://ambp.centre-mersenne.org/item/AMBP_1999__6_2_41_0/ %G en %F AMBP_1999__6_2_41_0
Nicolas Privault; Jiang-Lun Wu. Poisson stochastic integration in Hilbert spaces. Annales mathématiques Blaise Pascal, Tome 6 (1999) no. 2, pp. 41-61. https://ambp.centre-mersenne.org/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
[2] . Spectral families of quantum stochastic integrals. Communications in Mathematical Physics, 170:607-628, 1995. | Zbl | MR
[3] and . Infinite series of quantum spectral stochastic integrals. Journal of Operator Theory, 36:295-316, 1996. | Zbl | MR
[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. | Zbl | MR
[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. | Zbl | MR | Numdam
[7] . Symmetric Hilbert spaces and related topics, volume 261 of Lecture Notes in Mathematics. Springer Verlag, 1970. | Zbl | MR
[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. | Zbl | MR
[10] and . Quantum Itô's formula and stochastic evolutions. Communications in Mathematical Physics, 93:301-323, 1984. | Zbl | MR
[11] . Generalized Poisson functionals. Probab. Theory Related Fields, 77:1-28, 1988. | Zbl | MR
[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. | Zbl | MR
[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. | Zbl | MR
[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. | Zbl | MR | Numdam
[18] . On multiple Poisson stochastic integrals and associated Markov semi-groups. Probability and Mathematical Statistics, 3:217-239, 1984. | Zbl | MR
[19] . Construction du calcul stochastique sur un espace de Wiener abstrait. C. R. Acad. Sci. Paris Sér. I Math., 305:279-282, 1987. | Zbl | MR
[20] and . The construction of filtrations on abstract Wiener space. J. Funct. Anal., 143(1):10-32, 1997. | Zbl | MR
[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. | Zbl | MR | Numdam
