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Anal. 94 (1990) 74-92. 18. P. Lbvy: Leqons d’analyse fonctionnelle, Gauthier-Villars, Paris (1922). 19. N. Obata: White noise calculus and Fock space. L. N. Math. 1577 (1994). 20. H. Ouerdiane: Fonctionnelles analytiques avec conditions de croissance et application B l’analyse gaussienne. Japanese Journal of Math. Vol. 20, No. 1, (1994), 187-198 . 21. H. Ouerdiane: Noyaux et symboles d’opkrateurs sur des fonctionnelles analytiques gaussiennes. Japanese Journal of Math. Vol21. 1. (1995), 223-234 22.

Potthoff and L. Streit: White noise, An infinitedimensional calculus, Kluwer Academic Publishers Group,l993. 16. P. Krbe and H. Ouerdiane: Holomorphy and Gaussian analysis. Prkpublication de 1’Institut de mathkmatique de Jussieu. S. Univ. Paris 6 (1995). 17. H- H. Kuo, N. Obata and K. SaitB: Lkvy Laplacian of generalized functions on a nuclear space, 3. Funct. Anal. 94 (1990) 74-92. 18. P. Lbvy: Leqons d’analyse fonctionnelle, Gauthier-Villars, Paris (1922). 19. N. Obata: White noise calculus and Fock space.

26. L. Schwartz: Radon measures on arbitrary topological spaces and cylindrical measures, Oxford Univ. ,1973. STOCHASTIC GOLDEN RULE FOR A SYSTEM INTERACTING WITH A FERMI FIELD L. A. ROSCHIN Steklov Mathematical Institute Russian Academy of Sciences Gubkin St. V. VOLOVICH Steklov Mathematical Institute Russian Academy of Sciences Gubkin St. m We consider the (causally) normally ordered form of the quantum white noise equation for a Fermi white noise. We find a new form of the normally ordered equation for some class of Hamiltonians and we obtain the inner Langevin equation for such Hamiltonians.

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