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Vector-valued martingales and their applications

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Probability in Banach Spaces

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 526))

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References

  1. Cairoli, R. Une inégalité pour martingales à indices multiples et ses applications, Séminaire de Probabilité IV, Lecture Notes in Mathematics 124 (1970), 1–28, Springer Verlag.

    Google Scholar 

  2. Chacon, R.V. and Sucheston, L. On convergence of vector-valued asymptotic martingales. To appear.

    Google Scholar 

  3. Chatterji, S.D. Martingales of Banach-valued random variables, Bull. Amer. Math. Soc. 66 (1960), 395–98.

    Article  MathSciNet  MATH  Google Scholar 

  4. Chatterji, S.D. Martingale convergence and the Radon-Nikodym theorem in Banach spaces, Math. Scand. 22 (1968), 21–41.

    MathSciNet  MATH  Google Scholar 

  5. Chatterji, S.D. Differentiation along algebras, Manuscripta Math. 4 (1971), 213–224.

    Article  MathSciNet  MATH  Google Scholar 

  6. Chatterji, S.D. Les martingales et leurs applications analytiques, Ecole d'Eté de Probabilités: Processus stochastiques. Lecture Notes in Mathematics No. 307, Springer Verlag (1973).

    Google Scholar 

  7. Doob, J.L. Stochastic Processes. Wiley (1953).

    Google Scholar 

  8. Enflo, P. Banach spaces which can be given an equivalent uniformly convex norm, Israel J. Math. 13 (1972), 281–288.

    Article  MathSciNet  Google Scholar 

  9. Fernique, X. Intégrabilité des vecteurs gaussiens. C. R. Acad. Sc. Paris, Série A, 270 (1970), 1698–1699.

    MathSciNet  MATH  Google Scholar 

  10. Hoffmann-Jørgensen, J. Sums of independent Banach space valued random variables, Studia Math. 52 (1974), 159–186.

    MathSciNet  MATH  Google Scholar 

  11. Jain, N.C. and Kallianpur, G. A note on uniform convergence of stochastic processes, Ann. Math. Statist. 41 (1970), 1360–1362.

    Article  MathSciNet  MATH  Google Scholar 

  12. Jain, N.C. and Kallianpur, G. Norm convergent expansions for Gaussian processes in Banach spaces, Proc. Amer. Math. Soc. 25 (1970), 890–895.

    MathSciNet  MATH  Google Scholar 

  13. Kuelbs, J. Expansions of vectors in a Banach space related to Gaussian measures, Proc. Amer. Math. Soc. 27 (1971), 364–370.

    MathSciNet  MATH  Google Scholar 

  14. Kwapień, S. On Banach spaces containing co, Studia Math. 52 (1974), 187–188.

    MathSciNet  MATH  Google Scholar 

  15. Métivier, M. Martingales à valeurs vectorielles: applications à la dérivation des mesures vectorielles, Ann. Inst. Fourier XVII (1967), 175–208.

    Article  MATH  Google Scholar 

  16. Neveu, J. Martingales à temps discret. Masson (1972).

    Google Scholar 

  17. Phelps, R.R. Dentability and extreme points in Banach spaces, Jr. Funct. An. 17 (1974), 78–90.

    Article  MathSciNet  MATH  Google Scholar 

  18. Pisier, G. Martingales with values in uniformly convex spaces. To appear.

    Google Scholar 

  19. Scalora, F. Abstract martingale convergence theorems, Pacific J. Math. 11 (1961), 347–74.

    Article  MathSciNet  MATH  Google Scholar 

  20. Schaefer, H.H. Topological Vector Spaces. (1966) Third printing: Springer Verlag (1971).

    Google Scholar 

  21. Schwartz, L. Radon measures on arbitrary topological spaces and cylindrical measures, Tata Inst., Oxford University Press (1973).

    Google Scholar 

  22. Smythe, R.T. Strong laws of large numbers for r-dimensional arrays of random variables, Ann. Probability 1 (1973), 164–170.

    Article  MathSciNet  MATH  Google Scholar 

  23. Thomas, E. The Lebesgue-Nikodym theorem for vector valued Radon measures, Memoirs of AMS, No. 139, 1974.

    Google Scholar 

  24. Uhl, J.J. A survey of mean convergence of martingales of Pettis integrable functions. Vector and Operator valued measures and Applications, Edited by Tucker, D.H. and Maynard, H.B., Academic Press 1973, 379–385.

    Google Scholar 

  25. Walsh, J.B. A note on uniform convergence of stochastic processes. Proc. Amer. Math. Soc. 18 (1967), 129–132.

    Article  MathSciNet  MATH  Google Scholar 

  26. Wichura, M.J. A note on the convergence of series of stochastic processes, Ann. Probability 1 (1973), 180–182.

    Article  MathSciNet  MATH  Google Scholar 

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Anatole Beck

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© 1976 Springer-Verlag

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Chatterji, S.D. (1976). Vector-valued martingales and their applications. In: Beck, A. (eds) Probability in Banach Spaces. Lecture Notes in Mathematics, vol 526. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0082340

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  • DOI: https://doi.org/10.1007/BFb0082340

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  • Print ISBN: 978-3-540-07793-0

  • Online ISBN: 978-3-540-38256-0

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