Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J.M. Bismut and D. Michel: “Diffusions conditionnelles, I. Hypoellipticitè partielle”, J.F.A., Vol. 44, p. 147–211 (1981).
S. Kusuoka and D.W. Stroock: “The partial Malliavin calculus and its applications to nonlinear filtering”, Stochastics, Vol. 12, p. 83–142 (1984).
P. Malliavin: “Stochastic calculus of variations and hypoelliptic operators”, in the Proceedings of Internat. Conf. on Stoch. Diff. Equations of Kyoto, 1976, p. 195–263, Wiley, New York, 1978.
M. Chaleyat-Maurel: “Robustesse du filtre et calcul des variations stochastiques”, J.F.A., Vol. 68, p. 55–71 (1986).
P.A. Meyer: “Transformation de Riesz pour les lois gaussiennes”, Séminaire de Probe. XVIII, (1984) p. 179–193, L.N. in Math. Springer.
D. Ocone:-This volume
E. Pardoux: “Equations du filtrage nonlinéaire de la prediction et du lissage”, Stochastics, Vol. 6, p. 193–231.
H.H. Schaefer: Topological Vector Spaces. Graduate Texts in Math. Springer, 1971.
J. Szpirglas and G. Mazziotto: “Modèle général de filtrage nonlinéaire et equations differentielles stochastiques associeés”, A.I.H.P., Vol. XV, No. 2, p. 147–173, 1979.
L. Schwartz: Semi-martingales sur des variétés et martingales conformes sur des variétés analytiques complexes. L.N. in Math. No. 780, Springer, 1980.
A.S. Ustunel: “Extension of the Itô calculus via the Malliavin calculus”, to appear in Stochastics (1987).
A.S. Ustunel: “Une extension du calcul d'Itô via le calcul des variations stochastiques”, C.R.A.S. Paris, Vol. 300, Série I, p. 277–279 (1985).
A.S. Ustunel: “Some applications of stochastic integration in infinite dimension”, Stochastics, Vol. 7, p. 255–288 (1982).
A.S. Ustunel: “Representation of the distributions on the Wiener space and stochastic calculus of variations”, J.F.A., Vol. 70, p. 126–139 (1987).
A.S. Ustunel: “Formule de changement de variable pour l'intégrale anticipante de Skorohod”, C.R.A.S. Paris, Vol. 303, Ser. I., p. 329–331 (1986).
A.S. Ustunel: “Some applications of the Malliavin calculus to stochastic analysis”, Proceedings of the Conf. on Stochastic P.D.E., Trento, 1985, L.N. in Math., Vol.1236, 1987.
A.,S. Ustunel: “The Itô formula for anticipative processes with nonmonotonous time scale via the Malliavin Calculus”, to appear in Z.f.W.
A.S. Ustunel: “Construction du calcul stochastique sur un espace de Wiener abstrait”, C.R.A.S. Paris, Serie I, (1987).
S. Watanabe: Stochastic Differential Equations and Malliavin Calculus, Tata Inst. of Fundamental Research, Bombay, Springer, 1984.
A.Ju. Sevljakov: “The Itô formula for the extended stochastic integral”, Theory of Proba. and Math. Stat. No. 22, p. 163–174 (1981).
A.V. Skorohod: “On a generalization of a stochastic integral”, Theory of Proba. and its Applications, Vol. 20, p. 219–233 (1975).
P. Krée: “Continuité de la divergence dans les espaces de Sobolev relatifs à l'espace de Wiener”, C.R.A.S., t. 296, p. 833–837 (1983).
B. Gaveau and P. Trauber: “L'Intégrale stochastique comme operateur de divergence dans l'espace fonctionnel”, J.F.A., Vol. 46, p. 230–238 (1982).
D.R. Nualart: “A course on the Skorohod integral”, This volume.
D.R. Nualart and M. Zakai: “Generalized stochastic integrals and the Malliavin calculus”, Z.f.W. Vol. 73, p. 255–280 (1986).
Editor information
Rights and permissions
Copyright information
© 1988 Springer-Verlag
About this paper
Cite this paper
Ustunel, A.S. (1988). Some comments on the filtering of diffusions and the malliavin calculus. In: Korezlioglu, H., Ustunel, A.S. (eds) Stochastic Analysis and Related Topics. Lecture Notes in Mathematics, vol 1316. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0081934
Download citation
DOI: https://doi.org/10.1007/BFb0081934
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-19315-9
Online ISBN: 978-3-540-39186-9
eBook Packages: Springer Book Archive