Second order stochastic processes and the dilation theory in Banach spaces

Aleksander Weron

Annales de l'I.H.P. Probabilités et statistiques (1980)

  • Volume: 16, Issue: 1, page 29-38
  • ISSN: 0246-0203

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Weron, Aleksander. "Second order stochastic processes and the dilation theory in Banach spaces." Annales de l'I.H.P. Probabilités et statistiques 16.1 (1980): 29-38. <http://eudml.org/doc/77134>.

@article{Weron1980,
author = {Weron, Aleksander},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {dilations in Banach spaces; correlation function},
language = {eng},
number = {1},
pages = {29-38},
publisher = {Gauthier-Villars},
title = {Second order stochastic processes and the dilation theory in Banach spaces},
url = {http://eudml.org/doc/77134},
volume = {16},
year = {1980},
}

TY - JOUR
AU - Weron, Aleksander
TI - Second order stochastic processes and the dilation theory in Banach spaces
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1980
PB - Gauthier-Villars
VL - 16
IS - 1
SP - 29
EP - 38
LA - eng
KW - dilations in Banach spaces; correlation function
UR - http://eudml.org/doc/77134
ER -

References

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  1. [1] S.A. Cobanjan and A. Weron, Banach space valued stationary processes and their linear prediction, Dissertationes Math., t. 125, 1975, p. 1-45. Zbl0342.60031MR451373
  2. [2] J. Górniak and A. Weron, An analogue of Sz.-Nagy's dilation theorem, Bull. Acad. Polon. Sci., t. 24, 1976, p. 867-872. Zbl0343.47001MR425644
  3. [3] J. Górniak and A. Weron, Aronszajn-Kolmogorov type theorems for positive definite kernels in locally convex spaces, Studia Math., t. 69 (to appear). Zbl0473.46003MR647140
  4. [4] A. Makagon, An isomorphic theorem for Banach space valued stationary stochastic sequences, Bull. Acad. Polon. Sci., t. 26, 1978, p. 169-173. Zbl0385.60046MR488250
  5. [5] A. Makagon and F. Schmidt, A decomposition of the density of operator valued measure in Banach spaces, Bull. Acad. Polon. Sci. (to appear). Zbl0469.47040
  6. [6] V. Mandrekar and H. Salehi, Subordination of infinite-dimensional stationary stochastic processes, Ann. Inst. Henri Poincaré, t. 6, 1970, p. 115-130. Zbl0196.19101MR268953
  7. [7] P. Masani, Dilations as propagators of Hilbertian varieties, S. I. A. M. J. Anal., t. 9, 1978, p. 414-456. Zbl0391.47005MR500218
  8. [8] P. Masani, Propagators and dilations, Lecture Notes in Math., p. 656, 1978, p. 95-117, Springer Verlag. Zbl0388.46017MR521025
  9. [9] M. Metivier, Integrations with respect to processes of linear functionals, Séminaire de Rennes, 1975. 
  10. [10] M. Metivier and J. Pellaumail, Cylindrical stochastic integral, Séminaire de Rennes, 1976. 
  11. [11] W. Mlak, Dilations of Hilbert space operators (general theory), Dissertationes Math., t. 153, 1978, p. 1-61. Zbl0411.47004MR496046
  12. [12] W. Mlak and A. Weron, Dilations of Banach space operator valued functions, Ann. Polon. Math. (to appear). Zbl0454.47008MR599254
  13. [13] Nguyen Van Thu and A. Weron, Examples of non-stationary Banach space valued processes of second order, Lecture Notes in Math., t. 656, 1978, p. 171- 181, Springer Verlag. Zbl0394.60039
  14. [14] R. Payen, Functions aleatoires du second ordre a valeurs dans un espace de Hilbert, Ann. Inst. Henri Poincaré, t. 3, 1967, p. 323-396. Zbl0159.45901MR231438
  15. [15] M. Rosenberg, Mutual subordination of multivariate stationary processes over any locally compact Abelian group, Z. Wahrschernlichkeits theorie verw. Geb., t. 12, 1969, p. 333-343. Zbl0235.60038MR251790
  16. [16] F.H. Szafraniec, On the boundedness condition involved in dilation theory, Bull. Acad. Polon, t. 24, 1976, p. 877-881. Zbl0343.47003MR425645
  17. [17] F.H. Szafraniec, Dilations on involution semigroups, Proc. Amer. Math. Soc. Zbl0369.47004MR473873
  18. [18] F.H. Szafraniec, Apropos Professor Masani's talk, Lecture Notes in Math., t. 656, 1978, p. 245-249. Zbl0388.46018MR521034
  19. [19] A. Weron, Prediction theory in Banach spaces, Lecture Notes in Math., t. 472, 1975, p. 207-228, Springer Verlag. Zbl0314.60032MR394849
  20. [20] A. Weron, Remarks on positive-definite operator valued functions in Banach spaces, Bull. Acad. Polon. t. 24, 1976, p. 873-876. Zbl0343.47002MR433233

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