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On L2 and non-L2 multiple stochastic integration

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Stochastic Differential Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 36))

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References

  1. Astrauskas, A.: On stable self-similar fields (Russian). Liet. matem. rink. (to appear).

    Google Scholar 

  2. Dobrushin, R.L.: Gaussian and their subordinated self-similar random generalized fields. Ann. Probab. 7, (1979) 1–28.

    Google Scholar 

  3. Hida, T.: Stationary stochastic processes. Princeton, N.J.: Princeton University Press 1970.

    Google Scholar 

  4. Ito, K.: Multiple Wiener integral. J. Math. Soc. Japan 3, (1951) 157–164.

    Google Scholar 

  5. Ito, K.: Spectral type of shift transformations of differential process with stationary increments. Trans. Amer. Math. Soc. 81, (1956) 253–263.

    Google Scholar 

  6. Kabanov, Ju.M.: On extended stochastic integrals (Russian). Teor. Verojatn. i Primen. 20, (1975) 725–737

    Google Scholar 

  7. Kallianpur, G.: The role of reproducing kernel Hilbert spaces in the study of Gaussian processes. In: Hida T. (ed.). Advances in Probability and Related Topics, Vol. 2, p. 49–83. N.Y.: Dekker 1970.

    Google Scholar 

  8. Lass Fernandez, D.: Lorentz spaces, with mixed norms. J. Funct. Anal. 25, (1977) 125–146.

    Google Scholar 

  9. Meyer, P.-A.: Un cours sur les integrales stochastiques. Seminaire de Probabilites X. Lect. Notes Math. Vol. 511. Springer 1976.

    Google Scholar 

  10. Ogura, H.: Orthogonal functionals of the Poisson process. IEEE Trans. Inform. Theory IT-18, (1972) 473–480.

    Google Scholar 

  11. Okazaki, Y.: Wiener integral by stable random measures. Memoir Fac. Sci. Kyushu Univ. Ser. A, 33, (1979) 1–70.

    Google Scholar 

  12. Reed, M., Simon, B.: Methods of modern mathematical physics: Fourier analysis, self-adjointness. N.Y.: Academic Press 1975.

    Google Scholar 

  13. Surgailis, D.: On multiple Poisson stochastic integrals and associated Markov semigroups (to appear).

    Google Scholar 

  14. Surgailis, D.: On infinitely divisible self-similar random fields (to appear).

    Google Scholar 

  15. Taqqu, M.S.: Self-similar processes and related ultraviolet and infrared catastrophes. Techn. report No. 423 Cornell Univ. 1979.

    Google Scholar 

  16. Taqqu, M.S.: A representation for self-similar processes. Stoch. Processes Appl. 7, (1978) 55–64.

    Google Scholar 

  17. Wiener, N.: The homogeneous chaos. Amer. J. Math. 60, (1938) 897–936.

    Google Scholar 

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M. Arató D. Vermes A. V. Balakrishnan

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© 1981 Springer-Verlag

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Surgailis, D. (1981). On L2 and non-L2 multiple stochastic integration. In: Arató, M., Vermes, D., Balakrishnan, A.V. (eds) Stochastic Differential Systems. Lecture Notes in Control and Information Sciences, vol 36. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006424

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  • DOI: https://doi.org/10.1007/BFb0006424

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  • Print ISBN: 978-3-540-11038-5

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