Anticipative calculus for the Poisson process based on the Fock space

David Nualart; Josep Vives

Séminaire de probabilités de Strasbourg (1990)

  • Volume: 24, page 154-165

How to cite


Nualart, David, and Vives, Josep. "Anticipative calculus for the Poisson process based on the Fock space." Séminaire de probabilités de Strasbourg 24 (1990): 154-165. <>.

author = {Nualart, David, Vives, Josep},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {anticipative calculus; Fock space; Poisson space; Clark's formula},
language = {eng},
pages = {154-165},
publisher = {Springer - Lecture Notes in Mathematics},
title = {Anticipative calculus for the Poisson process based on the Fock space},
url = {},
volume = {24},
year = {1990},

AU - Nualart, David
AU - Vives, Josep
TI - Anticipative calculus for the Poisson process based on the Fock space
JO - Séminaire de probabilités de Strasbourg
PY - 1990
PB - Springer - Lecture Notes in Mathematics
VL - 24
SP - 154
EP - 165
LA - eng
KW - anticipative calculus; Fock space; Poisson space; Clark's formula
UR -
ER -


  1. 1. Eric A. Carlen and E. Pardoux, Differential Calculus and Integration by parts on Poisson space, preprint. Zbl0685.60056MR1052702
  2. 2. A. Dermoune, P. Kree and L. Wu, Calcul stochastique non adapté par rapport a la mesure aléatoire de Poisson, in "Séminaire de Probabilités XXII, Lecture Notes in Mathematics1321," pp. 477-484. Zbl0653.60045MR960543
  3. 3. B. Gaveau, P. Trauber, L'intégrale stochastique comme opérateur de divergence dans l'espace fonctionnel., J. Funct. Anal.46 (1982), 230-238. Zbl0488.60068MR660187
  4. 4. Yu.M. Kabanov, On extended stochastic integrals, Theory of Probability and its Applications20, 4 (1975), 710-722. Zbl0355.60047MR397877
  5. 5. J. Neveu, Processus Ponctuels., in "École d'Eté de Saint Flour 6, Lecture Notes in Math.598, Springer1977, 1976. Zbl0439.60044MR474493
  6. 6. D. Nualart and E. Pardoux, Stochastic Calculus with Anticipating Integrands, Probability Theory and Related Fields78 (1988), 535-581. Zbl0629.60061MR950346
  7. 7. D. Nualart and M. Zakai, Generalized Stochastic Integrals and the Malliavin Calculus, Probability Theory and Related Fields73 (1986), 255-280. Zbl0601.60053MR855226
  8. 8. H. Ogura, Orthogonal functionals of the Poisson processes, Trans IEEE Inf. Theory, IT-18,4 (1972), 473-481. Zbl0244.60044MR404572
  9. 9. J. Ruiz de Chavez, Sur la positivité de certains opérateurs, in "Séminaire de Probabilités XX, Lecture Notes in Mathematics1204," pp. 338-340. Zbl0649.60074MR942028
  10. 10. Skorohod A.V., On a generalization of a stochastic integral, Theor.Prob.Appl.20 (1975), 219-233. Zbl0333.60060MR391258
  11. 11. L. Wu, Construction de l'opérateur de Malliavin sur l'espace de Poisson, in "Séminaire de Probabilités XXI, Lectures Notes in Mathematics1247," pp. 100-113. Zbl0659.60079MR941978

Citations in EuDML Documents

  1. Nicolas Privault, Splitting the conservation process into creation and annihilation parts
  2. L. Decreusefond, N. Savy, Anticipative calculus with respect to filtered Poisson processes
  3. A. Dermoune, Wick product and stochastic partial differential equations with Poisson measure
  4. Cécile Ané, Clark–Ocone formulas and Poincaré inequalities on the discrete cube
  5. Florent Nicaise, Anticipative direct transformations on the Poisson space
  6. Jean Picard, Formules de dualité sur l'espace de Poisson

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.