@article{AIHPB_1981__17_1_31_0,
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 {\textsection} dilatations stationnaires {\guillemotright}},
journal = {Annales de l'institut Henri Poincar\'e. Section B. Calcul des probabilit\'es et statistiques},
pages = {31--49},
publisher = {Gauthier-Villars},
volume = {17},
number = {1},
year = {1981},
mrnumber = {610497},
zbl = {0489.60042},
language = {fr},
url = {http://www.numdam.org/item/AIHPB_1981__17_1_31_0/}
}
TY - JOUR AU - Truong-Van, B. TI - Une généralisation du théorème de Kolmogorov-Aronszajn « Processus $V$-bornés $q$-dimensionnels : domaine spectral § dilatations stationnaires » JO - Annales de l'institut Henri Poincaré. Section B. Calcul des probabilités et statistiques PY - 1981 SP - 31 EP - 49 VL - 17 IS - 1 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPB_1981__17_1_31_0/ LA - fr ID - AIHPB_1981__17_1_31_0 ER -
%0 Journal Article %A Truong-Van, B. %T Une généralisation du théorème de Kolmogorov-Aronszajn « Processus $V$-bornés $q$-dimensionnels : domaine spectral § dilatations stationnaires » %J Annales de l'institut Henri Poincaré. Section B. Calcul des probabilités et statistiques %D 1981 %P 31-49 %V 17 %N 1 %I Gauthier-Villars %U http://www.numdam.org/item/AIHPB_1981__17_1_31_0/ %G fr %F AIHPB_1981__17_1_31_0
Truong-Van, B. Une généralisation du théorème de Kolmogorov-Aronszajn « Processus $V$-bornés $q$-dimensionnels : domaine spectral § dilatations stationnaires ». Annales de l'institut Henri Poincaré. Section B. Calcul des probabilités et statistiques, Tome 17 (1981) no. 1, pp. 31-49. http://www.numdam.org/item/AIHPB_1981__17_1_31_0/
[1] , H-valued generalized functions and orthogonally scattered measures. Advances in Math., t. 19, n° 13, 1976, p. 382-412. | MR | Zbl
[2] , , , An operator version of a theorem of Kolmogorov. Pacific Journal of Math., t. 61, n° 2, 1975, p. 305-312. | MR | Zbl
[3] , 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 | Zbl
[4] , On the linear prediction problem for certain stochastic processes. ARTIV für MAT-Band, t. 4, n° 6, 1959, p. 45-53. | MR | Zbl
[5] , , Part I, Linear operators. Interscience. New York, Wiley, 1966.
[6] , Remarks on positive définite operator valued functions in linear spaces. Springer Verlag, Lectures Notes in Math., t. 656, 1978, p. 37-44. | MR | Zbl
[7] , , Aronszajn-Kolmogorov type theorem for positive définite kernels in locally corvex spaces preprint (to appear in Studia Math.), 1978. | EuDML | MR | Zbl
[8] , Measure theory. Van Nostrand, New York, 1950. | MR | Zbl
[9] , Probability theory. Van Nostrand (2e édition), 1960, Princeton, Toronto, London, Melbourne. | MR | Zbl
[10] , On generalized positive definite functions. Proc. London Math. Soc., t. 3, n° 15, 1965. p. 373-384. | MR | Zbl
[11] , On generalization of second-order stationarity. Proc. London. Math. Soc., t. 3, 15, 1965, p. 385-398. | MR | Zbl
[12] , Linear operators in V H-spaces. Trans. Amer. Math. Soc., t. 116, 1965, p. 167-180. | MR | Zbl
[13] , , 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 | Zbl
[14] , Utilisation des méthodes de l'Analyse spectrale à la prévision linéaire de certains processus stationnaires. Rev. CETHEDEC, t. 16, 1968, p. 137-148. | MR
[15] , , Harmonizability, V-boundedness and stationary dilation of stochastic Processes. Indiana. Univ. Math. J., t. 27, n° 1, 1978, p. 37-50. | MR | Zbl
[16] , Dilatations as propagators of Hilbertian varieties. SIAM J. Math. Anal., t. 9, n° 3, june 1978, p. 414-456. | MR | Zbl
[17] , Stochastic processes as Fourier transforms for stochastic measures. Ann. Acad. Sci. Fenn. Series A. I. Math., t. 591, 1975. | MR | Zbl
[18] , 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 | Zbl
[19] , On stationary dilations and the linear prediction of certain stochastic processes. Comm. Physico. Math., t. 45, n° 4, 1975, p. 111-130. | MR | Zbl
[20] , On the linear prediction problems of certain non-stationary stochastic processes. Math. Scand., t. 39, 1976, n° 1, p. 146-160. | MR | Zbl
[21] , On orthogonally scattered dilations of bounded vector measures. Ann. Acad. Sci. Fenn. Séries 1. I Math., vol. 3, 1977, p. 43-52. | MR | Zbl
[22] , p-majorisierbare vektorwertige Masse. Wiss Z. F. Schiller, Univ. Jena Math. Naturwiss. Reihe, t. 18, 1969, p. 243-247. | MR | Zbl
[23] , Masse mit werten in einem Hilbertraum. Wiss Z. F. Schiller, Univ. Jena Math. Naturwiss. Reihe, t. 18, 1969, p. 253-257. | MR | Zbl
[23 bis] , 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] , Spectral Analysis of Abstract functions. SIAM The theory of Proba. and. Appl., t. IV, n° 3, 1959, p. 271-287. | MR | Zbl
[25] , Real and complex Analysis. Mac Graw Hill. New York, 1974. | MR | Zbl
[26] , , 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 | Zbl
[27] , Prediction theory in Banach spaces. Lecture Notes in Math., t. 472, 1975, p. 207-228, Springer-Verlag. Berlin. | MR | Zbl
[28] , Contribution à l'étude des processus V-bornés multidimensionnels. Thèse de 3e Cycle, Université P. Sabatier, Toulouse, 1979.
