Subordination of infinite-dimensional stationary stochastic processes
Mandrekar, V. ; Salehi, H.
Annales de l'I.H.P. Probabilités et statistiques, Tome 6 (1970), p. 115-130 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPB_1970__6_2_115_0,
     author = {Mandrekar, Vidyadhar and Salehi, H.},
     title = {Subordination of infinite-dimensional stationary stochastic processes},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {6},
     year = {1970},
     pages = {115-130},
     mrnumber = {268953},
     zbl = {0196.19101},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_1970__6_2_115_0}
}

Mandrekar, V.; Salehi, H. Subordination of infinite-dimensional stationary stochastic processes. Annales de l'I.H.P. Probabilités et statistiques, Tome 6 (1970) pp. 115-130. http://gdmltest.u-ga.fr/item/AIHPB_1970__6_2_115_0/

[1] J. Dixmier, Les algèbres d'opérateurs dans l'espace Hilbertien. Gauthier-Villars, Paris, 1957. | MR 94722 | Zbl 0088.32304

[2] R. Gangolli, Wide-sense stationary sequences of distributions on Hilbert space and factorization of operator valued functions. J. Math. Mech., 12, 1963, 893-910. | MR 161349 | Zbl 0124.33704

[3] U. Grenander and G. Szegö, Toeplitz forms and their applications. University of California Press, California, 1958. | MR 94840 | Zbl 0080.09501

[4] P.R. Halmos, A Hilbert space problem book. D. Van Nostrand, New Jersey, 1967. | MR 208368 | Zbl 0144.38704

[5] G. Kallianpur and V. Mandrekar, Multiplicity and representation theory of purely non-deterministic stochastic processes. Theor. Prob. Appl., 10, 1965, 553-581. | MR 192563 | Zbl 0171.38902

[6] A.N. Kolmogorov, Stationary sequences in Hilbert space. Bull. Math. Univ. Moscow, 2, 1941, 1-40. | Zbl 0063.03291

[7] V. Mandrekar and H. Salehi, The square-integrability of operator-valued functions with respect to a non-negative operator-valued measure and the Kolmogorov isomorphism theorem. To appear in J. Math. Mech. | MR 267069

[8] P. Masani, Sur la fonction génératrice d'un processus stochastique vectoriel. C. R. Acad. Sci., 249, 1959, 360-362. | MR 107299 | Zbl 0088.10903

[9] P. Masani, Recent trends in multivariate prediction theory. Multivariate Analysis. Academic Press, New York, 1966, 351-382. | MR 214228 | Zbl 0216.46706

[10] P. Masani, The normality of time-invariant, subordinative operators in a Hilbert space. Bull. Amer. Math. Soc., 71, 1965, 546-550. | MR 177304 | Zbl 0143.16503

[11] R.F. Matveev, On multidimensional regular stationary processes. Theor. Prob. Appl., 6, 1961, 149-165. | Zbl 0211.21601

[12] F.J. Murray and J. Von Neumann On rings of operators. Ann. Math., 37, 1936, 116-229. | JFM 62.0449.03 | MR 1503275 | Zbl 0014.16101

[13] J. Neveu, Processus aléatoires gaussiens. Les Presses de l'Université de Montréal, Montreal, 1968. | MR 272042 | Zbl 0192.54701

[14] R. Payen, Fonctions aléatoires du second ordre à valeurs dans un espace de Hilbert. Ann. Inst. Henri Poincaré, III, 1967, 323-396. | Numdam | MR 231438 | Zbl 0159.45901

[15] J.B. Robertson and M. Rosenberg, The decomposition of matrix-valued measures. Mich. Math. J., 15, 1968, 353-368. | MR 239044 | Zbl 0167.14602

[16] M. Rosenberg, Square integrability of matrix-valued functions with respect to a non-negative definite hermitian measure. Duke Math. J., 31, 1964, 291-298. | MR 163346 | Zbl 0129.08902

[17] M. Rosenberg, Mutual subordination of multivariate stationary processes over any locally compact Abelian group. Z. Wahrscheinlichkeitstheorie verw. Geb., 12, 1969, 333-343. | MR 251790 | Zbl 0235.60038

[18] H. Salehi, The Hellinger square-intergrability of matrix-valued measures with respect to a non-negative hermitian measure. Ark. Mat., 7, 1967, 299-303. | MR 233951 | Zbl 0159.18902

[19] H. Salehi, Application of the Hellinger integrals to q-variate stationary stochastic processes. Ark. Mat., 7, 1967, 305-311. | MR 236991 | Zbl 0164.19001