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Convergence en loi des suites d'intégrales stochastiques sur l'espace \(\mathbb{D}\) 1 de Skorokhod
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  • Published: 01 February 1989

Convergence en loi des suites d'intégrales stochastiques sur l'espace \(\mathbb{D}\) 1 de Skorokhod

  • A. Jakubowski1,
  • J. Mémin2 &
  • G. Pages3 

Probability Theory and Related Fields volume 81, pages 111–137 (1989)Cite this article

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Summary

For sequences of stochastic Integrals K n.X n, functional limit Theorems are presented, these results hold under simple natural conditions.

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References

  1. Billingsley, P.: Convergence of probability measures. New York: Wiley 1968

    MATH  Google Scholar 

  2. Dellacherie, C., Meyer, P.A.: Probabilités et potentiel, tome 2. Paris: Hermann 1980

    MATH  Google Scholar 

  3. Follmer, H.: Calcul d'Ito sans probabilités; séminaire de probabilités XV. Lect. Notes Math., vol. 850. Berlin Heidelberg New York: Springer 1981

    MATH  Google Scholar 

  4. Jacob, J.: Calcul stochastique et problèmes de martingales. Lect. Notes Math., vol. 714. Berlin Heidelberg New York: Springer 1979

    Google Scholar 

  5. Jacod, J.: Théorèmes limite pour les processus; cours de l'école d'été de Saint-Flour. Lect. Notes Math., vol. 1117. Berlin Heidelberg New York: Springer 1985

    Google Scholar 

  6. Jacob, J., Memin, J., Metivier, M.: On tightness and stopping times. Stoch. Proc. Appl. 14, 109–146 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  7. Jakubowski, A.: On the Skorokhod topology. Ann. Inst. Henri Poincaré, Nouv. Ser., Sect. B22, 263–285 (1986)

    MathSciNet  MATH  Google Scholar 

  8. Lindvall, T.: Weak convergence of probability measures and random functions in the function Space D[0,∞[. J. Appl. Probab. 10, 109–121 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  9. Liptser, R.Ch., Shiryayev, A.N.: On a problem of necessary and sufficient conditions in the functional central limit theorem for local martingales. Z. Wahrscheinlichkeitstheor. Verw. Geb. 59, 312–318 (1982)

    Article  MathSciNet  Google Scholar 

  10. McLeish, D.L.: An extended martingale invariance principle. Ann. Probab. 6, 144–150 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  11. Memin, J.: Théorèmes limite fonctionnels pour les processus de vraisemblance (cadre asymptotiquement non gaussien). Publications IRMAR. 1985 (Rennes 1986)

  12. Meyer, P.A., Zheng, W.A.: Tightness criteria for laws of semimartingales. Ann. Inst. Henri Poincaré, Nouv. Ser., Sect. B20, 353–372 (1984)

    MathSciNet  MATH  Google Scholar 

  13. Pages, G.: Un théorème de convergence fonctionnelle pour les intégrales stochastiques. Séminaires de Probabilités XX. Lect. Notes Math., vol. 11. Berlin Heidelberg New York: Springer 1986

    MATH  Google Scholar 

  14. Rootzen, H.: On the functional limit theorem for martingales. Z. Wahrscheinlichkeitstheor. Verw. Geb. 51, 79–94 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  15. Stominski, L.: Approximation of predictable characteristics of processes with filtrations. Preprint, Univ. Torun, Pologne, 1985

    Google Scholar 

  16. Skorokhod, A.V.: Limit theorems for stochastic processes. Th. Probab. Appl. I, 423–439 (1956)

    MATH  Google Scholar 

  17. Strassen, V.: The existence of probability measures with given marginals. Ann. Math. Stat. 36, 423–439 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  18. Stricker, C.: Caractérisation des semimartingales. Séminaire de probabilité XVIII. Lect. Notes Math., vol. 1059. Berlin Heidelberg New York: Springer 1984

    Google Scholar 

  19. Stricker, C.: Lois de semimartingales et critères de compacité. Séminaires de probabilités XIX. Lect. Notes Math., vol. 1123. Berlin Heidelberg New York: Springer 1985

    MATH  Google Scholar 

  20. Yor, M.: Les inégalités de sousmartingales comme conséquences de la relation de domination. Stochastics, 3, 1–17 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  21. Avram, F.: Weak convergence of the variations, iterated integrals and Doléans-Dade exponentials of sequences of semimartingales. Ann. Probab. 16, 246–250 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  22. Jacod, J., Shiryaev, A.N.: Limit theorems for stochastic processes. Berlin Heidelberg New York: Springer 1987

    Book  MATH  Google Scholar 

  23. Strasser, H.: Martingale difference arrays and stochastic integrals. Probab. Th. Rel. Fields 72, 83–98 (1986)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. M. Copernicus University, ul. Chopina 12/18, Pl-87100, Toruń, Poland

    A. Jakubowski

  2. Campus de Beaulieu, Université de Rennes 1, IRMAR, F-35042, Rennes, France

    J. Mémin

  3. Laboratoire de Probabilités, Université P. et M. Curie, 4 Place Jussieu, F-75230, Paris 05, France

    G. Pages

Authors
  1. A. Jakubowski
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  2. J. Mémin
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  3. G. Pages
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Jakubowski, A., Mémin, J. & Pages, G. Convergence en loi des suites d'intégrales stochastiques sur l'espace \(\mathbb{D}\) 1 de Skorokhod. Probab. Th. Rel. Fields 81, 111–137 (1989). https://doi.org/10.1007/BF00343739

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  • Received: 14 July 1986

  • Revised: 11 July 1988

  • Published: 01 February 1989

  • Issue Date: February 1989

  • DOI: https://doi.org/10.1007/BF00343739

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Keywords

  • Natural Condition
  • Stochastic Process
  • Probability Theory
  • Limit Theorem
  • Statistical Theory
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