Integrals related to stationary processes and cylindrical martingales

J. Pellaumail; A. Weron

Annales de l'I.H.P. Probabilités et statistiques (1979)

  • Volume: 15, Issue: 2, page 127-146
  • ISSN: 0246-0203

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Pellaumail, J., and Weron, A.. "Integrals related to stationary processes and cylindrical martingales." Annales de l'I.H.P. Probabilités et statistiques 15.2 (1979): 127-146. <http://eudml.org/doc/77116>.

@article{Pellaumail1979,
author = {Pellaumail, J., Weron, A.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {operator valued functions; quadratic integral; stochastic integral; stationary processes; square integrable cylindrical martingales},
language = {eng},
number = {2},
pages = {127-146},
publisher = {Gauthier-Villars},
title = {Integrals related to stationary processes and cylindrical martingales},
url = {http://eudml.org/doc/77116},
volume = {15},
year = {1979},
}

TY - JOUR
AU - Pellaumail, J.
AU - Weron, A.
TI - Integrals related to stationary processes and cylindrical martingales
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1979
PB - Gauthier-Villars
VL - 15
IS - 2
SP - 127
EP - 146
LA - eng
KW - operator valued functions; quadratic integral; stochastic integral; stationary processes; square integrable cylindrical martingales
UR - http://eudml.org/doc/77116
ER -

References

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  2. [ChW1] S.A. Chobanyan and A. Weron, Stationary processes in pseudo-Hilbertian space (in Russian), Bull. Acad. Polon., t. 21, 1973, p. 847-854. Zbl0269.60034
  3. [ChW2] S.A. Chobanyan and A. Weron, Banach space valued stationary processes and their linear prediction. Dissertationes Math., t. 125, 1975, p. 1-45. Zbl0342.60031MR451373
  4. [Dou] R.G. Douglas, On factoring positive operator functions. J. Math. Mech., t. 16, 1966, p. 119-126. Zbl0149.09901MR209887
  5. [DuS] N. Dunford and J.T. Schwartz, Linear operators. Part. 1. Intersciences Publishers, 1967. Zbl0084.10402
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  7. [Mas] 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. Indiana University Mathematical Journal. vol. 20, n° 6, December 1970. Zbl0252.46040MR267069
  8. [Mas] P. Masani, Quasi isometric measures and their applications. Bull. Amer. Math. Soc., vol. 76, n° 3, 1970. Zbl0207.44001MR259062
  9. [Met1] M. Metivier, Integration with respect to processes of linear fonctionnals. Séminaire de Probabilité de Rennes, 1975. 
  10. [Met2] M. Metivier, Cylindrical martingales and stochastic integrals. Lecture on the conference. Probability Theory on vector spaces. Trzebieszowice, 1977 (non published). 
  11. [MeP1] M. Metivier and J. Pellaumail, Cylindrical stochastic integral. Séminaire de Rennes, 1976. 
  12. [MeP2] M. Metivier and J. Pellaumail, A basic course on stochastic integration. Séminaire de Rennes, 1978. 
  13. [Pel] J. Pellaumail, Sur la dérivation d'une mesure vectorielle. Bull. Soc. Math. France, t. 98, 1970, p. 305-318. Zbl0193.43003MR276431
  14. [Tre] F. Treves, Topological vector spaces, distributions and kernels. Academic Press, 1967. Zbl0171.10402MR225131
  15. [Wel] J.N. Welsh, Constructions of the Hilbert space L2,M for operator measures. Proc. Symp. on vector and Operator measures. A. Utah, 1972. 
  16. [Wer1] A. Weron, Prediction theory in Banach spaces. Lecture Notes in Math., vol. 472, 1975, p. 207-227. Zbl0314.60032MR394849
  17. [Wer2] A. Weron, Remarks on positive-definite operator valued functions in Banach spaces. Bull. Acad. Polon., t. 24, 1976, p. 873-876. Zbl0343.47002MR433233
  18. [Wer3] A. Weron, Second order stochastic processes and the dilation theory in Banach spaces (to appear). Zbl0445.60010MR575174
  19. [Yos] K. Yosida, Functionnal analysis. Second printing, Springer Verlag, 1966. 

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