Application des variables non commutatives des calculs formels en statistique non linéaire
Thèses d'Orsay, no. 93 (1980) , 138 p. 
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     author = {Lamnabhi Lagarrigue, Fran\c{c}oise},
     title = {Application des variables non commutatives des calculs formels en statistique non lin\'eaire},
     series = {Th\`eses d'Orsay},
     publisher = {Universit\'e de Paris-Sud Centre d'Orsay},
     number = {93},
     year = {1980},
     language = {fr},
     url = {http://archive.numdam.org/item/BJHTUP11_1980__0093__P0_0/}
}
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Lamnabhi Lagarrigue, Françoise. Application des variables non commutatives des calculs formels en statistique non linéaire. Thèses d'Orsay, no. 93 (1980), 138 p. http://numdam.org/item/BJHTUP11_1980__0093__P0_0/

[A1] R. Abe - Statistical mechanics - University of Tokyo Press, 1975.

[A2] L. Arnold - Stochastic differential equations - Wiley Interscience, New-York, 1974, chapitre 10. | Zbl

[B1] J. C. Barrett- The use of functional in the analysis of non linear physical models-J. Elect. Control, 15, 1963, p. 567-615. | DOI

[B2] C. M. Bender et I.-T. Wu - Anharmonic oscillator - Phys. Rev. 184, 1969, p. 1231. | DOI

[B3] L. Bieberbach -Analytische Fortsetzung - Berlin, Springer Verlag, 1975. | Zbl

[B4] M. Bixon et R. Zwanzig - Brownian motion of a non linear oscillator - J. Stat. Phys., 3, 1971, p. 245-260. | DOI

[B5] R. Bonhour et N. Foucherot - Mise en oeuvre informatique d'une nouvelle méthode de calcul en automatique non linéaire - Thèse 3ème cycle, Université Paris VII, Paris, 1977.

[B6] D.C.C. Bover - Moment equation methods for non linear stochastic systems - J. Math. Anal. and Appl., 65, 1978, p. 306-320. | Zbl | DOI

[B7] R.-W. Brockett - Volterra series and geometric control theory - Automatica, 12, 1976, p. 167-176. | Zbl | DOI

[B8] A.B. Budgor - Studies in non linear stochastic processes. I. Approxiate solutions of non linear stochastic differential equations by the method of statistical linearization - J. Stat. Phys., 15, 1976, p. 355-375. | DOI

[B9] A.B. Budgor et B.J. West - Connection between perturbation theory projection operator technics, and statistical linearization for non linear systems - Phys. Review A, 17, 1978, p. 370-376. | DOI

[D1] J. Dieudonné - Eléments d'analyse III, Gauthiers-Villars, Paris, 1974

[D2] F.J. Dyson - Divergence of perturbation theory in quantum electro-dynamic - Phys. Rev., 85, 1952, p. 631. | Zbl | DOI

[E1] S. Eilenberg - Automata, languages and machines - Vol. A, Academic Press, New York, 1974. | Zbl

[E2] W.N. Edward - Symbolic and algebraic computation - Lecture Notes in computer science, Springer Verlag, n° 72, Eurosam 1979. | Zbl

[Fl] R.P. Feynman et A.R. Hibbs - Quantum mechanics and path integrals - Mc Graw-Hill Book Company, 1965. | Zbl

[F2] J. Fitch - A Survey of symbolic computation in physics - dans Lecture Notes in Computer Science, Springer-Verlag, n° 72, Berlin Eurosam 1979, p. 30-41.

[F3] M. Fliess - Sur divers produits de séries formelles - Bull. Soc. Math., France, 102, 1974, p. 181-191. | Zbl | Numdam | DOI

[F4] M. Fliess - Séries formelles non commutatives et automatique non linéaire - dans Séries formelles en variables non commutatives et applications, Ed. J. Berstel, Paris, L.I.T.P. et E.N.S.T.A., 1978, p. 69-118. | Zbl

[F5] M. Fliess - Développements fonctionnels en indéterminées non commutatives de solutions d'équations différentielles non linéaires forcées - C.R. Acad. Sc., 287,1978,Série A p. 1133-1135. | Zbl

[F6] M. Fliess - Formule dormant les moments des solutions d'équations différentielles stochastiques non linéaires - Rapport interne n°19, 1978.

[F7] M. Fliess - A Remark on the transfer functions and the realization of homogeneous continuous-time non linear systems IEEE Trans. Autom. Control, AC-24, 1979, p. 507-508. | Zbl

[F8] M. Fliess - Stabilité d'un type élémentaire d'équations différentielles stochastiques à bruits vectoriels - (à paraître). | Zbl

[G1] E. G. Gilbert - Functional Expansions for the response of non linear differential systems - IEEE Trans. Automat. Control, AC-22, 1977, p. 909-921. | Zbl

[G2] W. Gröbner - Die Lie-Reihen und ihre Anwendungen - 2ème édition, VEB Deutscher Verlag der Wissenschaften, Berlin, 1967. | Zbl

[I1] K. Ito - Stochastic Differentials - Appl. Math. Optimization, 1, 1975, p. 374-381. | Zbl

[K1] D.E. Knuth - The Art of computer programming - Vol. 1 : Fundamental Algorithms, Addison-Wesley Massachusetts, 1977.

[K2] P.I. Kuznetsov, R.L. Stratonovich et V.I. Tikhonov - Non Linear transformations of stochastic processes, Pergamon Press, Oxford, 1975. | Zbl

[L1] F. Lamnabhi et M. Lamnabhi - Détermination algébrique des noyaux de Volterra associés à certains systèmes non linéaires- Recerche di Automatica, 10, 1979.

[L2] F. Langouche, D. Roekaerts et E. Tirapegui - Functional integral method for stochastic fields - Physica, 95A, 1979, p. 252-274. | DOI

[L3] S.C. Liu - Solution of Fokker-Planck equation with applications in non linear random vibration - Bell. System Tech. J., 48, 1969, p. 2031-2051. | Zbl | DOI

[M1] K. Matsuo - Brownian motion of non linear oscillators : the projection operator method and its application to a double-well-potential oscillator - J. Stat. Phys., 18, 6, 1978, p. 535-555. | DOI

[M2] G.E. Mitzel, S.J. Clancy et W.J. Rugh - On Transfer function representations for homogeneous non linear systems, IEEE Trans. Autom. Control, AC 24, 1979, p. 242-249. | Zbl

[M3] J.B. Morton et Corrsin - Experimental confirmation of the applicability of the Fokker-Planck equation to a non linear oscillator, J. Math. Phys., 10, 1969, p. 361-368. | DOI

[M4] J.B. Morton et S. Corrsin - Consolidated expansions for estimating the response of a randomly driven non linear oscillator - J. Stat. Phys., 2, 1970, p. 153-194. | DOI

[N1] A. Nayfeh - Perturbation methods - Wiley-Interscience, New York, 1973. | Zbl

[U1] C.A. Uzes - Mechanical response and the initial value problem, J. Math. Phys., 19, 1978, p. 2232-2238. | Zbl | DOI

[V1] H.L. Van Trees - Functional technics for the analysis of the non linear behavior of phased-locked loops, Proc. IEEE, 52, 1964, p. 894-911. | DOI

[W1] R.M. Wilcox et R. Bellman - Truncation and preservation of moment properties for Fokker-Planck moment equations - J. Math. Anal. Appl., 32, 1970, p. 532-542. | Zbl | DOI

[W2] H.W. Wyld - Formulation of the theory of turbulence in an incompressible fluid - Ann. Phys., 14, 1961, p. 143. | Zbl

[W3] E. Wong et M. Zakai - On the relation between ordinary and stochastic differential equations - Int. J. Engin. Sci., 3, 1965, p. 213-229. | Zbl | DOI