Une généralisation du théorème de Kolmogorov-Aronszajn «Processus -bornés -dimensionnels : domaine spectral § dilatations stationnaires»
Annales de l'I.H.P. Probabilités et statistiques (1981)
- Volume: 17, Issue: 1, page 31-49
- ISSN: 0246-0203
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topTruong-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 17.1 (1981): 31-49. <http://eudml.org/doc/77155>.
@article{Truong1981,
author = {Truong-Van, B.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {nonstationary processes; locally compact abelian group; dilation type results},
language = {fre},
number = {1},
pages = {31-49},
publisher = {Gauthier-Villars},
title = {Une généralisation du théorème de Kolmogorov-Aronszajn «Processus $V$-bornés $q$-dimensionnels : domaine spectral § dilatations stationnaires»},
url = {http://eudml.org/doc/77155},
volume = {17},
year = {1981},
}
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'I.H.P. Probabilités et statistiques
PY - 1981
PB - Gauthier-Villars
VL - 17
IS - 1
SP - 31
EP - 49
LA - fre
KW - nonstationary processes; locally compact abelian group; dilation type results
UR - http://eudml.org/doc/77155
ER -
References
top- [1] J.L. Abreu, H-valued generalized functions and orthogonally scattered measures. Advances in Math., t. 19, n° 13, 1976, p. 382-412. Zbl0338.46037MR410894
- [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. Zbl0324.46041MR405167
- [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. Zbl0074.12502MR84883
- [4] H. Cramer, On the linear prediction problem for certain stochastic processes. ARTIV für MAT-Band, t. 4, n° 6, 1959, p. 45-53. Zbl0093.14404MR163348
- [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. Zbl0383.47006MR521020
- [7] J. Gorniak, A. Weron, Aronszajn-Kolmogorov type theorem for positive définite kernels in locally corvex spaces preprint (to appear in Studia Math.), 1978. Zbl0473.46003MR647140
- [8] P.R. Halmos, Measure theory. Van Nostrand, New York, 1950. Zbl0040.16802MR33869
- [9] M. Lœve, Probability theory. Van Nostrand (2e édition), 1960, Princeton, Toronto, London, Melbourne. Zbl0095.12201MR123342
- [10] R.M. Loynes, On generalized positive definite functions. Proc. London Math. Soc., t. 3, n° 15, 1965. p. 373-384. Zbl0138.39102MR173933
- [11] R.M. Loynes, On generalization of second-order stationarity. Proc. London. Math. Soc., t. 3, 15, 1965, p. 385-398. Zbl0211.21502MR176531
- [12] R.M. Loynes, Linear operators in V H-spaces. Trans. Amer. Math. Soc., t. 116, 1965, p. 167-180. Zbl0138.39103MR192359
- [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. Zbl0252.46040MR267069
- [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. MR272041
- [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. Zbl0353.60036MR461657
- [16] P. Masani, Dilatations as propagators of Hilbertian varieties. SIAM J. Math. Anal., t. 9, n° 3, june 1978, p. 414-456. Zbl0391.47005MR500218
- [17] H. Niemi, Stochastic processes as Fourier transforms for stochastic measures. Ann. Acad. Sci. Fenn. Series A. I. Math., t. 591, 1975. Zbl0307.60034MR445593
- [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. Zbl0327.28009MR399410
- [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. Zbl0339.60036MR410893
- [20] H. Niémi, On the linear prediction problems of certain non-stationary stochastic processes. Math. Scand., t. 39, 1976, n° 1, p. 146-160. Zbl0349.60037MR426128
- [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. Zbl0367.46041MR632060
- [22] A. Pietsch, p-majorisierbare vektorwertige Masse. Wiss Z. F. Schiller, Univ. Jena Math. Naturwiss. Reihe, t. 18, 1969, p. 243-247. Zbl0217.09302MR264028
- [23] R. Rogge, Masse mit werten in einem Hilbertraum. Wiss Z. F. Schiller, Univ. Jena Math. Naturwiss. Reihe, t. 18, 1969, p. 253-257. Zbl0203.44301MR265550
- [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. Zbl0089.32602MR123357
- [25] W. Rudin, Real and complex Analysis. Mac Graw Hill. New York, 1974. Zbl0278.26001MR344043
- [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. Zbl0325.60038MR386004
- [27] A. Weron, Prediction theory in Banach spaces. Lecture Notes in Math., t. 472, 1975, p. 207-228, Springer-Verlag. Berlin. Zbl0314.60032MR394849
- [28] B. Truong-Van, Contribution à l'étude des processus V-bornés multidimensionnels. Thèse de 3e Cycle, Université P. Sabatier, Toulouse, 1979.
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