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A Skorohod - like representation in infinite dimensions

Part of the Lecture Notes in Mathematics book series (LNM,volume 1153)

Abstract

Every discrete parameter Banach space-valued martingale may be embedded in a continuous parameter martingale which has continuous sample paths and is adapted to the σ-fields generated by one-dimensional Brownian motion.

Keywords

  • Brownian Motion
  • Probability Space
  • Standard Brownian Motion
  • Infinite Dimension
  • Strong Markov Property

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Azéma, J. and Yor, M., Une solution simple au probléme de Skorohod, Sem. Probab. XIII, Lecture notes in Math., Springer (1979).

    Google Scholar 

  2. Bass, R.F., Skorohod imbedding via stochastic integrals, Sem. Probab. XVII, Lecture notes in Math., Springer (1983).

    Google Scholar 

  3. Baxter, J.R. and Chacon, R.V., Potentials of stopped distributions, Illinois J. of Math., 18 (1974), 649–656.

    MathSciNet  MATH  Google Scholar 

  4. Burkholder, D.L., A sharp inequality for martingale transforms, Ann. Probability 7 (1979), 858–863.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Burkholder, D.L., A geometrical characterization of Banach spaces in which martingale difference sequences are unconditional, Ann. Probability 9 (1981), 997–1001.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Chacon, R.V. and Walsh, J.B., One-dimensional potential embedding, Sem. Probab. X, Lecture notes in Math., Springer (1976).

    Google Scholar 

  7. Dubins, L.E., On a problem of Skorohod, Ann. Math. Statist. 39 (1968), 2094–2097.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. Falkner, N., On Skorohod embedding in n-dimensional Brownian motion by means of natural stopping times, Sem. Probab. XIV, Lecture notes in Math., Springer (1980).

    Google Scholar 

  9. Ikeda, N. and Watanabe, S., Stochastic differential equations and diffusion processes, North Holland, Amsterdam, 1981.

    MATH  Google Scholar 

  10. Kiefer, J., Skorohod embedding of Multivariate RV’s, and the Sample DF, Z. Wahrscheinlichkeitstheorie verw. Geb. 24 (1972), 1–35.

    CrossRef  MATH  Google Scholar 

  11. Pisier, G., Martingales with values in uniformly convex spaces, Israel J. Math. 20 326–350.

    Google Scholar 

  12. Root, D.H., The existence of certain stopping times of Brownian motion, Ann. Math. Statist. 40 (1969), 715–718.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. Rost, H., The stopping distributions of a Markov process, Invent. Math. 14 (1971), 1–16.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. Skorohod, A., Studies in the Theory of Random Processes, Addison Wesley, Reading, 1965.

    Google Scholar 

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© 1985 Springer-Verlag

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McConnell, T.R. (1985). A Skorohod - like representation in infinite dimensions. In: Beck, A., Dudley, R., Hahn, M., Kuelbs, J., Marcus, M. (eds) Probability in Banach Spaces V. Lecture Notes in Mathematics, vol 1153. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074960

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  • DOI: https://doi.org/10.1007/BFb0074960

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15704-5

  • Online ISBN: 978-3-540-39645-1

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