A calculus on Fock space and its probabilistic interpretations

Bulletin des Sciences Mathematiques

Volumn 123, Issue 2, 1999, Pages 97-114

  Privault, Nicolas ^a  

^a UNIVERSITÉ D EVRY VAL D ESSONNE   (France)

Author keywords

Fock space; Poisson process; Stochastic calculus of variations; Wiener process

Indexed keywords

EID: 0033074853     PISSN: 00074497     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0007-4497(99)80016-5     Document Type: Article

References (10)

1. [1] Bouleau (N.) and Hirsch (F.). - Dirichlet Forms and Analysis on Wiener Space. - Berlin, New York, de Gruyter, 1991.
2. [2] Carlen (E.) and Pardoux (E.). - Differential calculus and integration by parts on Poisson space, In Stochastics, Algebra and Analysis in Classical and Quantum Dynamics, p. 63-73. - Kluwer, 1990.
3. [3] León (J.A.) and Tudor (C.). - A chaos approach to the anticipating calculus for the Poisson process, Stochastics and Stochastic Reports, 62, 1998, p. 217-250.
4. [4] Nualart (D.). - The Malliavin Calculus and Related Topics. - Berlin, New York, Springer Verlag, 1995 (Probability and its Applications).
5. [5] Nualart (D.) and Vives (J.). - Anticipative calculus for the Poisson process based on the Fock space, In Séminaire de Probabilités XXIV, J. Azéma, P.A. Meyer and M. Yor, eds., p. 154-165. - Berlin, Springer Verlag, 1990 (Lecture Notes in Mathematics, 1426).
6. [6] Privault (N.). - Chaotic and variational calculus in discrete and continuous time for the Poisson process, Stochastics and Stochastics Reports, 51, 1994, p. 83-109.
7. [7] Privault (N.). - A transfer principle from Wiener to Poisson space and applications, J. Funct. Anal., 132, 1995, p. 335-360.
8. [8] Privault (N.). - Calculus on Fock space and a quantum non-adapted Itô formula, C.R. Acad. Sc. Paris, Série I, 323, 1996, p. 927-932.
9. [9] Stroock (D.). - Homogeneous chaos revisited, In Séminaire de Probabilités XXI, p. 1-7. - Berlin, Springer Verlag, 1987 (Lecture Notes in Mathematics, 1247).
10. [10] Ustünel (A.S.). - An Introduction to Analysis on Wiener Space. - Berlin, New York, Springer-Verlag, 1995 (Lecture Notes in Mathematics, 1610).