Abstract
This work consists of the applications of the infinite dimensional stochastic calculus to the following problems:Construction of the E∞-flows of the finite dimensional diffusions with regular coefficients, a simple and short proof of the generalized Ito-Stratonovitch formula,probabilistic solutions of the heat and Schrodinger1s equations in the space of the distributions,diffusions depending on a parameter and the reduc tion of the unnormalized density equation of the filter ing of non-linear diffusions into a deterministic Cauchy problem depending on a parameter.
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References
A. Badrikian: “Séminaire sur les Fonctions Aléatoi res Linéaires et les Mesures Cylindriques”. Lect. Notes in Math. Vol. 139. Springer-Verlag. Berlin-Heidelberg-New York, 1970.
J-M. Bismut: “A generalized formula of I to and some other properties of stochastic flows”. Zeitschr-für Wahrsch. verve. Geb. 55, 331–350 (1981).
C. Dellacherie and P. A. Meyer: Probalilités et Potentiel, Chapitres I-IV. Hermann, Paris, 1975.
C. Dellacherie and P. A. Meyer: Probabilités et Potentiel, Chapitres V-VIII. Hermann, Paris, 1980.
A. Grothendieck: “Produits tensoriels topologiques et espaces nucleaires”. Mem. Amer. Math. Soc. No. 6 (1955)
M. Métivier and J. Pellaumail: Stochastic Integration. Academic Press, 1980.
H.H. Schaefer: Topological Vector Spaces. Graduate Texts in Math. Springer-Verlag. Berlin-Heidelberg-New York, 1970.
L. Schwartz: Théorie Aes Distributions. Hermann, Paris, 1973.
A. S. Üstünel: “Calcul stochastique sur les espaces nucléaires et ses applications”. Thése de Doctorat d’ Etat, Université de Paris V I, 1981.
A. S. Üstünel: “Formule de Feynman-Kac stochastique”. C.R. Acad. Sc. Paris, t. 292, p. 595–597 (1981).
A.S. Üstünel: “Stochastic integration on nuclear spaces and its applications”. Preprint, to appear in A.I.H.P.
A.S. Ostunel::“a characterization of semimartingales on the nuclear spaces”. Preprint, to appear in Zeit. für Wahrs. and verve Geb.
A. S. Üstünel: “Some applications of stochastic integration in infinite dimension I”. Pre-print. to appear in Stochastics.
A.S. Üstünel: “Some applications of stochastic inte-gration in infinite dimension II”. Preprint. To appear in Stochastics.
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© 1983 D. Reidel Publishing Company
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Ustunel, A.S. (1983). Some Applications of Stochastic Calculus on the Nuclear Spaces to the Nonlinear Problems. In: Bucy, R.S., Moura, J.M.F. (eds) Nonlinear Stochastic Problems. NATO ASI Series, vol 104. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7142-4_36
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DOI: https://doi.org/10.1007/978-94-009-7142-4_36
Publisher Name: Springer, Dordrecht
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