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Planar seminartingales obtained by transformations of two-parameter martingales

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Séminaire de Probabilités XXIII

Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 1372))

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Abstract

In this paper we study the weak local submartingale property and the quasimartingale property of processes obtained by the composition of a two-parameter continuous martingale by c2-functions whose second derivative is convex.

The work of Nguyen Minh Duc was done during a stay at the University of Barcelona (Spain).

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References

  1. Brennan, M. D. "Planar semimartingales". Journal of multivariate Analysis 9, 465–486 (1979).

    Article  MathSciNet  MATH  Google Scholar 

  2. Cairoli, R. and Walsh, J. B. "Stochastic integrals in the plane". Acta Math. 134, 111–183 (1975).

    Article  MathSciNet  MATH  Google Scholar 

  3. Dellacheire, C. et Meyer, P. A. "Probabilités et Potentiel". Vol. 2 Hermann. Paris (1980).

    Google Scholar 

  4. Föllmer, H. "Quasimartingales à deux indices". C. R. Acad. Sc. Paris. Sér 1, t. 288, 61–64 (1979).

    MathSciNet  MATH  Google Scholar 

  5. Meyer, P. A. "Un cours sur les intégrales stochastiques". Sém. de Probab. X. Lecture Notes in Math. 511. Springer Verlag. Berlin-Heidelberg-New York (1980).

    MATH  Google Scholar 

  6. Nguyen Minh Duc and Nguyen Xuan Loc. "On the transformation of a martingale with a two-dimensional parameter set by convex functions". Z. Wahr. un Verw. Gebiete 66, 19–24 (1984).

    Article  MATH  Google Scholar 

  7. Nguyen Minh Duc and Nguyen Xuan Loc. "Characterization of functions which transform Brownian sheet into planar semimartingales". Preprint Series n.o 26. Inst. of Math. and Inst. of Computer Scien. and Cybernetics. Hanoi 1985.

    Google Scholar 

  8. Nualart, D. "On the quadratic variation of two-parameter continuous martingales". Annals of Probab. Vol 12, n.o 2, 445–457 (1984).

    Article  MathSciNet  MATH  Google Scholar 

  9. Nualart, D. "Une formule d'Itô pour les martingales continues à deux indices et quelques applications". Ann. de l'Institut H. Poincaré Vol. 20, 3, 251–275 (1984).

    MathSciNet  MATH  Google Scholar 

  10. Nualart, D. and Utzet, F. "A property of two-parameter martingales with path-independent variation". Stoch. Proc. and their Appl. 24, 31–49 (1987).

    Article  MathSciNet  MATH  Google Scholar 

  11. Nualart D., Sanz, M. and Zakai M. "On the relations between increasing functions associated with two-parameter continuous martingales". Tech. Report n.o 190. Center for Stochastic Processes. University of North Carolina at Chapel Hill (1987).

    Google Scholar 

  12. Sanz, M. "Local time for two-parameter continuous martingales with respect to the quadratic variation". Annals of Probab. Vol 16, n.o 2, (1981).

    Google Scholar 

  13. Sanz, M. "r-variations for two-parameter continuous martingales and Itô's formula" Preprint. (1987).

    Google Scholar 

  14. Yoeurp, Ch. "Compléments sur les temps locaux et les quasimartingales". Astérisque 52–53. 197–218 (1978).

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Computer Science and Cybernetics Nghia Do - Tu Liem, Hanoi R.S., Vietnam

    Nguyen Minh Duc

  2. Facultat de Matemàtiques, Universitat de Barcelona, Gran Via, 585, 08007, Barcelona, Spain

    D. Nualart & M. Sanz

Authors
  1. Nguyen Minh Duc
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  2. D. Nualart
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  3. M. Sanz
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Editor information

Jacques Azéma Marc Yor Paul André Meyer

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© 1989 Springer-Verlag

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Duc, N.M., Nualart, D., Sanz, M. (1989). Planar seminartingales obtained by transformations of two-parameter martingales. In: Azéma, J., Yor, M., Meyer, P.A. (eds) Séminaire de Probabilités XXIII. Lecture Notes in Mathematics, vol 1372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084000

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  • DOI: https://doi.org/10.1007/BFb0084000

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51191-5

  • Online ISBN: 978-3-540-46176-0

  • eBook Packages: Springer Book Archive

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