Une généralisation du théorème de Kolmogorov-Aronszajn « Processus V-bornés q-dimensionnels : domaine spectral § dilatations stationnaires »
Truong-Van, B.
Annales de l'I.H.P. Probabilités et statistiques, Tome 17 (1981), p. 31-49 / Harvested from Numdam
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Publié le : 1981-01-01
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     author = {Truong-Van, B.},
     title = {Une g\'en\'eralisation du th\'eor\`eme de Kolmogorov-Aronszajn \guillemotleft{} Processus $V$-born\'es $q$-dimensionnels : domaine spectral \S\ dilatations stationnaires \guillemotright{}},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {17},
     year = {1981},
     pages = {31-49},
     mrnumber = {610497},
     zbl = {0489.60042},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIHPB_1981__17_1_31_0}
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Truong-Van, B. Une généralisation du théorème de Kolmogorov-Aronszajn « Processus $V$-bornés $q$-dimensionnels : domaine spectral § dilatations stationnaires ». Annales de l'I.H.P. Probabilités et statistiques, Tome 17 (1981) pp. 31-49. http://gdmltest.u-ga.fr/item/AIHPB_1981__17_1_31_0/

[1] J.L. Abreu, H-valued generalized functions and orthogonally scattered measures. Advances in Math., t. 19, n° 13, 1976, p. 382-412. | MR 410894 | Zbl 0338.46037

[2] G.D. Allen, F.J. Narcowich, J.O. Williams, An operator version of a theorem of Kolmogorov. Pacific Journal of Math., t. 61, n° 2, 1975, p. 305-312. | MR 405167 | Zbl 0324.46041

[3] S. Bochner, Stationarity, boundedness, almost periodicity of random valued functions. Proceed. of the 3rd Berkeley symposium on math. stat. and proba. Univ. of California Press, 1956, p. 7-27. | MR 84883 | Zbl 0074.12502

[4] H. Cramer, On the linear prediction problem for certain stochastic processes. ARTIV für MAT-Band, t. 4, n° 6, 1959, p. 45-53. | MR 163348 | Zbl 0093.14404

[5] N. Dunford, J.T. Schwartz, Part I, Linear operators. Interscience. New York, Wiley, 1966.

[6] J. Gorniak, Remarks on positive définite operator valued functions in linear spaces. Springer Verlag, Lectures Notes in Math., t. 656, 1978, p. 37-44. | MR 521020 | Zbl 0383.47006

[7] J. Gorniak, A. Weron, Aronszajn-Kolmogorov type theorem for positive définite kernels in locally corvex spaces preprint (to appear in Studia Math.), 1978. | MR 647140 | Zbl 0473.46003

[8] P.R. Halmos, Measure theory. Van Nostrand, New York, 1950. | MR 33869 | Zbl 0040.16802

[9] M. Lœve, Probability theory. Van Nostrand (2e édition), 1960, Princeton, Toronto, London, Melbourne. | MR 123342 | Zbl 0095.12201

[10] R.M. Loynes, On generalized positive definite functions. Proc. London Math. Soc., t. 3, n° 15, 1965. p. 373-384. | MR 173933 | Zbl 0138.39102

[11] R.M. Loynes, On generalization of second-order stationarity. Proc. London. Math. Soc., t. 3, 15, 1965, p. 385-398. | MR 176531 | Zbl 0211.21502

[12] R.M. Loynes, Linear operators in V H-spaces. Trans. Amer. Math. Soc., t. 116, 1965, p. 167-180. | MR 192359 | Zbl 0138.39103

[13] V. Mandrekar, H. Salehi, The square integrability of operator valued functions with respect to a non-negative operator valued measure and the Kolmogorov Isomorphism theorem. Indiana. Univ. Math. J., t. 20, n° 6, 1970, p. 545-563. | MR 267069 | Zbl 0252.46040

[14] M.M. Martin, Utilisation des méthodes de l'Analyse spectrale à la prévision linéaire de certains processus stationnaires. Rev. CETHEDEC, t. 16, 1968, p. 137-148. | MR 272041

[15] A.G. Miamée, H. Salehi, Harmonizability, V-boundedness and stationary dilation of stochastic Processes. Indiana. Univ. Math. J., t. 27, n° 1, 1978, p. 37-50. | MR 461657 | Zbl 0353.60036

[16] P. Masani, Dilatations as propagators of Hilbertian varieties. SIAM J. Math. Anal., t. 9, n° 3, june 1978, p. 414-456. | MR 500218 | Zbl 0391.47005

[17] H. Niemi, Stochastic processes as Fourier transforms for stochastic measures. Ann. Acad. Sci. Fenn. Series A. I. Math., t. 591, 1975. | MR 445593 | Zbl 0307.60034

[18] H. Niémi, On the support of a bimesure and orthogonally scattered vector measures. Ann. Acad. Sci. Fenn. Series A. I. Math., t. I, 1975, p. 249-275. | MR 399410 | Zbl 0327.28009

[19] H. Niémi, On stationary dilations and the linear prediction of certain stochastic processes. Comm. Physico. Math., t. 45, n° 4, 1975, p. 111-130. | MR 410893 | Zbl 0339.60036

[20] H. Niémi, On the linear prediction problems of certain non-stationary stochastic processes. Math. Scand., t. 39, 1976, n° 1, p. 146-160. | MR 426128 | Zbl 0349.60037

[21] H. Niémi, On orthogonally scattered dilations of bounded vector measures. Ann. Acad. Sci. Fenn. Séries 1. I Math., vol. 3, 1977, p. 43-52. | MR 632060 | Zbl 0367.46041

[22] A. Pietsch, p-majorisierbare vektorwertige Masse. Wiss Z. F. Schiller, Univ. Jena Math. Naturwiss. Reihe, t. 18, 1969, p. 243-247. | MR 264028 | Zbl 0217.09302

[23] R. Rogge, Masse mit werten in einem Hilbertraum. Wiss Z. F. Schiller, Univ. Jena Math. Naturwiss. Reihe, t. 18, 1969, p. 253-257. | MR 265550 | Zbl 0203.44301

[23 bis] M. Rosenberg, Minimum trace quasi-isometric dilations of operator-valued measures and minimum trace orthogonally-scattered dilations of multivariate vector measures. Jour. of Multivariate Anal. (à paraître).

[24] A.Yu. Rozanov, Spectral Analysis of Abstract functions. SIAM The theory of Proba. and. Appl., t. IV, n° 3, 1959, p. 271-287. | MR 123357 | Zbl 0089.32602

[25] W. Rudin, Real and complex Analysis. Mac Graw Hill. New York, 1974. | MR 344043 | Zbl 0278.26001

[26] D. Tjöstheim, J.B. Thomas, Some properties and examples of random processes that are almost wide sense stationary. I. E. E. E. Trans. Inf. Th., t. 21, 1975, p. 257-262. | MR 386004 | Zbl 0325.60038

[27] A. Weron, Prediction theory in Banach spaces. Lecture Notes in Math., t. 472, 1975, p. 207-228, Springer-Verlag. Berlin. | MR 394849 | Zbl 0314.60032

[28] B. Truong-Van, Contribution à l'étude des processus V-bornés multidimensionnels. Thèse de 3e Cycle, Université P. Sabatier, Toulouse, 1979.