A generalized Itô-Ventzell formula. Application to a class of anticipating stochastic differential equations

Daniel Ocone; Etienne Pardoux

Annales de l'I.H.P. Probabilités et statistiques (1989)

  • Volume: 25, Issue: 1, page 39-71
  • ISSN: 0246-0203

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Ocone, Daniel, and Pardoux, Etienne. "A generalized Itô-Ventzell formula. Application to a class of anticipating stochastic differential equations." Annales de l'I.H.P. Probabilités et statistiques 25.1 (1989): 39-71. <http://eudml.org/doc/77339>.

@article{Ocone1989,
author = {Ocone, Daniel, Pardoux, Etienne},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Itô-Ventzell formula for anticipating processes; Stratonovich stochastic integrals; ordinary differential equation with random coefficients},
language = {eng},
number = {1},
pages = {39-71},
publisher = {Gauthier-Villars},
title = {A generalized Itô-Ventzell formula. Application to a class of anticipating stochastic differential equations},
url = {http://eudml.org/doc/77339},
volume = {25},
year = {1989},
}

TY - JOUR
AU - Ocone, Daniel
AU - Pardoux, Etienne
TI - A generalized Itô-Ventzell formula. Application to a class of anticipating stochastic differential equations
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1989
PB - Gauthier-Villars
VL - 25
IS - 1
SP - 39
EP - 71
LA - eng
KW - Itô-Ventzell formula for anticipating processes; Stratonovich stochastic integrals; ordinary differential equation with random coefficients
UR - http://eudml.org/doc/77339
ER -

References

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  1. [1] R.A. Adams, Sobolev Spaces, Acad. Press, 1975. Zbl0314.46030MR450957
  2. [2] J.M. Bismut, A Generalized Formula of Itô and Some Other Properties of Stochastic Flows, Z. Wahrschein. Werw. Geb., Vol. 55, 1981, pp. 331-350. Zbl0456.60063MR608026
  3. [3] J.M. Bismut and D. Michel, Diffusions conditionnelles, J. Funct. Anal., Vol. 44, 1981, pp. 174-211 and 45, 1982, pp. 274-292. Zbl0475.60061
  4. [4] T. Jeulin and M. YorEds., Grossissements de filtrations: exemples et applications, Lecture Notes in Mathematics, Vol. 1118, Springer Verlag, 1985. Zbl0547.00034MR884713
  5. [5] H. KunitaStochastic Differential Equations and Stochastic Flow of Diffeomorphisms, in Ecole d'été de Probabilités de St-Flour, P. L. Hennequin Ed., Lecture Notes in Mathematics, Vol. 1097, Springer-Verlag, 1984, pp. 144-300. Zbl0554.60066MR876080
  6. [6] D. NualartNoncausal Stochastic Integrals and Calculus, in Stochastic Analysis and Related Topics, H. KOREZLIOGLU and A.S. Ustunel Eds., Lecture Notes in Mathematics, No. 1316, Springer-Verlag, 1988, pp. 80-129. Zbl0644.60043MR953794
  7. [7] D. Nualart and E. Pardoux, Stochastic Calculus with Anticipating Integrands Prob. Theory and Rel. Fields, Vol. 78, 1988, pp. 535-581. Zbl0629.60061MR950346
  8. [8] S. Ogawa, Sur la question d'existence de solutions d'une equation différentielle stochastique de type noncausal, J. Math.Kyoto Univ., Vol. 24, 1984, pp. 699-704. Zbl0603.60059MR775980

Citations in EuDML Documents

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  1. Martin T. Barlow, Peter Imkeller, On some sample path properties of Skorohod integral processes
  2. Marco Ferrante, Triangular stochastic differential equations with boundary conditions
  3. Y. Ouknine, A. Berkaoui, Sur l'approximation de la solution d'une équation différentielle stochastique anticipative
  4. Axel Grorud, David Nualart, Marta Sanz-Solé, Hilbert-valued anticipating stochastic differential equations
  5. Jean Picard, Transformations et équations anticipantes pour les processus de poisson

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