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References
Baklan, V. V.: Integration of random functions with respect to a Wiener random measure. Theory Probability and Math. Statist. 29, 13–17 (1984).
Berger, M. A.: A Malliavin-type anticipative stochastic calculus. Preprint.
Berger, M. A., Mizel, V. J.: An extension of the stochastic integral. Ann. Probab. 10, 435–450 (1982).
Bismut, J. M.: Mécanique Aléatoire. Lecture Notes in Math. 866, Springer-Verlag 1981.
Bismut, J. M.: Martingales, the Malliavin Calculus and hypoellipticity under general Hörmander's conditions. Z. Wahrschein. verw. Gebiete 56, 469–505 (1981).
Blum, J.: Clark-Haussmann formulas for the Wiener sheet. Diss. ETH No. 8157.
Clark, J. M. C.: The representation of functionals of Brownian motion by stochastic integrals. Ann. Math. Statist. 41, 1282–1295 (1970); 42, 1778 (1971).
Daletskii, Yu. L., Paramonova, S. N.: Stochastic integrals with respect to a normally distributed additive set function. Soviet Math. Dokl. 14, 96–100 (1973).
Daletskii, Yu. L., Paramonova, S. N.: On a formula from the theory of Gaussian measures and on the estimation of stochastic integrals. Theory Prob. Appl. 19, 812–817 (1974).
Föllmer, H.: Calcul d'Itô sans probabilités. Lecture Notes in Math. 850, 143–150 (1981).
Gaveau, B., Trauber, P.: L'intégrale stochastique comme opérateur de divergence dans l'espace fonctionnel. J. Functional Anal. 46, 230–238 (1982).
Gihman, J. I.: On the representation of functionals of a Wiener sheet by stochastic integrals. Lecture Notes in Control and Inf. Sci. 81, 37–49 (1984).
Hajek, B., Wong, E.: Multiple Stochastic Integrals: Projection and Iteration. Z. Wahrshein. verw. Gebiete 63, 349–368 (1983).
Hitsuda, M.: Formula for Brownian Partial Derivatives. Publ. Fac. of Integrated Arts and Sciences Hiroshima Univ., 3, 1–15 (1979).
Huang, S. T., Cambanis, S.: Gaussian processes: Nonlinear analysis and stochastic calculus. Lecture Notes in Math. 695, 165–177 (1978).
Ikeda, N., Watanabe, S.: An introduction to Malliavin's Calculus. Proc. Taniguchi Inter. Symp. on Stoch. Analysis. Katata and Kyoto, 1982, pp. 1–52 (1984).
Itô, K.: Multiple Wiener integral. J. Math. Soc. Japan 3, 157–169 (1951).
Jeulin, T.: Semi-Martingales and Grossissement d'une Filtration. Lecture Notes in Math. 833. Springer-Verlag 1980.
Krée, M.: Propriété de trace en dimension infinie, d'espaces du type Sobolev. Bull. Soc. Math. France, 105, 141–163 (1977).
Krée, M., Krée, P.: Continuité de la divergence dans les espaces de Sobolev relatifs à l'espace de Wiener. C.R.A.S. 296, 833–836 (1983).
Kunita, H.: On backward stochastic differential equations. Stochastics, 6, 293–313 (1982).
Kuo, H. H., Russek, A.: White Noise Approach to Stochastic Integration. Preprint.
Kusuoka, S.: The non-linear transformation of Gaussian measure on Banach space and its absolute continuity (I). J. Fac. Sci. Univ. Tokyo, IA, 29, 567–597 (1982).
Malliavin, P.: Stochastic calculus of variations and hypoelliptic operators. Proc. Inter. Symp. on Stoch. Diff. Equations. Kyoto, 1976, pp. 195–263 (1978).
Meyer, P. A.: Transformations de Riesz pour les lois Gaussiennes. Lecture Notes in Math. 1059, 179–193 (1984).
Nualart, D., Pardoux, E.: Stochastic calculus with anticipating integrands. Preprint.
Nualart, D., Zakai, M.: Generalized stochastic integrals and the Malliavin Calculus. Probability Theory and Rel. Fields, 73, 255–280 (1986).
Nualart, D., Zakai, M.: Generalized multiple stochastic integrals and the representation of Wiener Functionals. Preprint.
Ocone, D.: Malliavin Calculus and stochastic integral representation of diffusion processes. Stochastics 12, 161–185 (1984).
Ogawa, S.: Une remarque sur l'approximation de l'intégrale stochastique du type noncausal par une suite des intégrales de Stieltjes. Tôhoku Math. Journ. 36, 41–48 (1984).
Ogawa, S.: Quelques propriétés de l'intégrale stochastique du type noncausal. Japan J. Appl. Math. 1, 405–416 (1984).
Ogawa, S.: The stochastic integral of noncausal type as an extension of the symmetric integrals. Japan J. Appl. Math. 2, 229–240 (1984).
Ogawa, S.: Sur la question d'existence de solutions d'une équation différentielle stochastique du type noncausal. J. Math. Kyoto Univ. 24–1, 699–704 (1984).
Pardoux, E., Protter, Ph.: A two-sided stochastic integral and its calculus. Probab. Th. Rel. Fields 76, 15–49 (1987).
Ramer, R.: On non-linear trnsformations of Gaussian measures. J. Funct. Anal. 15, 166–187 (1974).
Rosinski, J.: On stochastic integration by series of Wiener integrals. Technical Report No. 112, Univ. North Carolina, Chapel Hill (1985).
Sekiguchi, T., Shiota, Y.: L2-theory of noncausal stochastic integrals. Math. Rep. Toyama Univ. 8, 119–195 (1985).
Sekiguchi, T., Shiota, Y.: On a class of the universally integrable random functions. Tohôku Math. Journ. 38, 357–364 (1986).
Sevljakov, A. Ju.: The Itô formula for the extended stochastic integral. Theory Prob. and Math. Statist. 22, 163–174 (1981).
Shiota, Y.: A linear stochastic integral equation containing the extended Itô integral. Math. Rep. Toyama Univ. 9, 43–65 (1986).
Sigekawa, I.: Derivatives of Wiener functionals and absolute continuity of induced measures. J. Math. Kyoto Univ. 20–2, 263–289 (1980).
Shigekawa, I.: de Rham-Hodge-Kodaira's decomposition on an abstract Wiener space. Preprint.
Skorohod, A. V.: On a generalization of a stochastic integral. Theory Prob. and Appl. XX, 219–233 (1975).
Stinespring, W. F.: A sufficient condition for an integral operator to have a trace. J. Reine and Angew. Math. 200, 200–207 (1958).
Sugita, H.: Sobolev spaces of Wiener functionals and Malliavin's calculus. J. Math. Kyoto Univ. 25–1, 31–48, (1985).
Sznitman, A. S.: Martingales dépendant d'un parà metre: une formule d'Itô. Z. Wahrschein. verw. Gebiete 60, 41–70 (1982).
Ustunel, A. S.: La formule de changement de variable pour l'intégrale anticipante de Skorohod. C.R.A.S. Paris, 303, Série I, no 7 (1986).
Ustunel, A. S.: Representation of the distributions on Wiener space and stochastic calculus of variations. J. Funct. Anal. 70, 126–139 (1987).
Ustunel, A. S.: The Itô Formula for Anticipative Processes with Nonmonotonous Time Scale via the Malliavin Calculus. Preprint.
Watanabe, S.: Lectures on stochastic differential equations and Malliavin Calculus. Tata Institute of Fundamental Research. Springer-Verlag, 1984.
Wong, E., Zakai, M.: Martingales and stochastic integrals for processes with a multi-dimensional parameter. Z. Wahrschein. verw. Gebiete 29, 109–122 (1974).
Yor, M.: Sur quelques approximations d'intégrales stochastiques. Lecture Notes in Math. 581, 518–528 (1977).
Zakai, M.: The Malliavin Calculus. Acta Appl. Math. 3–2, 175–207 (1985).
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Nualart, D. (1988). Nonclausal stochastic integrals and 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/BFb0081930
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