Subordination of infinite-dimensional stationary stochastic processes

V. Mandrekar; H. Salehi

Annales de l'I.H.P. Probabilités et statistiques (1970)

  • Volume: 6, Issue: 2, page 115-130
  • ISSN: 0246-0203

How to cite

top

Mandrekar, V., and Salehi, H.. "Subordination of infinite-dimensional stationary stochastic processes." Annales de l'I.H.P. Probabilités et statistiques 6.2 (1970): 115-130. <http://eudml.org/doc/76913>.

@article{Mandrekar1970,
author = {Mandrekar, V., Salehi, H.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {probability theory},
language = {eng},
number = {2},
pages = {115-130},
publisher = {Gauthier-Villars},
title = {Subordination of infinite-dimensional stationary stochastic processes},
url = {http://eudml.org/doc/76913},
volume = {6},
year = {1970},
}

TY - JOUR
AU - Mandrekar, V.
AU - Salehi, H.
TI - Subordination of infinite-dimensional stationary stochastic processes
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1970
PB - Gauthier-Villars
VL - 6
IS - 2
SP - 115
EP - 130
LA - eng
KW - probability theory
UR - http://eudml.org/doc/76913
ER -

References

top
  1. [1] J. Dixmier, Les algèbres d'opérateurs dans l'espace Hilbertien. Gauthier-Villars, Paris, 1957. Zbl0088.32304MR94722
  2. [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. Zbl0124.33704MR161349
  3. [3] U. Grenander and G. Szegö, Toeplitz forms and their applications. University of California Press, California, 1958. Zbl0080.09501MR94840
  4. [4] P.R. Halmos, A Hilbert space problem book.D. Van Nostrand, New Jersey, 1967. Zbl0144.38704MR208368
  5. [5] G. Kallianpur and V. Mandrekar, Multiplicity and representation theory of purely non-deterministic stochastic processes. Theor. Prob. Appl., 10, 1965, 553-581. Zbl0171.38902MR192563
  6. [6] A.N. Kolmogorov, Stationary sequences in Hilbert space. Bull. Math. Univ. Moscow, 2, 1941, 1-40. Zbl0063.03291
  7. [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. Zbl0252.46040MR267069
  8. [8] P. Masani, Sur la fonction génératrice d'un processus stochastique vectoriel. C. R. Acad. Sci., 249, 1959, 360-362. Zbl0088.10903MR107299
  9. [9] P. Masani, Recent trends in multivariate prediction theory. Multivariate Analysis. Academic Press, New York, 1966, 351-382. Zbl0216.46706MR214228
  10. [10] P. Masani, The normality of time-invariant, subordinative operators in a Hilbert space. Bull. Amer. Math. Soc., 71, 1965, 546-550. Zbl0143.16503MR177304
  11. [11] R.F. Matveev, On multidimensional regular stationary processes. Theor. Prob. Appl., 6, 1961, 149-165. Zbl0211.21601
  12. [12] F.J. Murray and J. von NeumannOn rings of operators. Ann. Math., 37, 1936, 116-229. Zbl0014.16101MR1503275JFM62.0449.03
  13. [13] J. Neveu, Processus aléatoires gaussiens. Les Presses de l'Université de Montréal, Montreal, 1968. Zbl0192.54701MR272042
  14. [14] R. Payen, Fonctions aléatoires du second ordre à valeurs dans un espace de Hilbert. Ann. Inst. Henri Poincaré, III, 1967, 323-396. Zbl0159.45901MR231438
  15. [15] J.B. Robertson and M. Rosenberg, The decomposition of matrix-valued measures. Mich. Math. J., 15, 1968, 353-368. Zbl0167.14602MR239044
  16. [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. Zbl0129.08902MR163346
  17. [17] M. Rosenberg, Mutual subordination of multivariate stationary processes over any locally compact Abelian group. Z. Wahrscheinlichkeitstheorie verw. Geb., 12, 1969, 333-343. Zbl0235.60038MR251790
  18. [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. Zbl0159.18902MR233951
  19. [19] H. Salehi, Application of the Hellinger integrals to q-variate stationary stochastic processes. Ark. Mat., 7, 1967, 305-311. Zbl0164.19001MR236991

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.