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Part of the book series: NATO ASI Series ((ASIC,volume 372))

Abstract

Outlined is a bi-measure theoretic framework, including the fundamental Grothendieck inequality and factorization theorem of which self-contained proofs are presented. Stochastic integrators have a natural description in this framework.

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Bibliography

  1. R.C. Blei. Fractional dimensions and bounded fractional forms. Mem. Am. Math Soc., 57(331), 1985.

    Google Scholar 

  2. R.C. Blei. An elementary proof of the Grothendieck inequality. Proc. Amer. Math. Soc., 100:58–60,1987.

    Article  MathSciNet  MATH  Google Scholar 

  3. R.C. Blei. Multi-linear measure theory and the Grothendieck factorization theorem. Proc. London Math. Soc., 56:529–546,1988.

    Article  MathSciNet  MATH  Google Scholar 

  4. R.C. Blei. Multi-linear measure theory and multiple stochastic integration.Prob. Th. Rel. Fields, 81:569–584,1989.

    Article  MathSciNet  MATH  Google Scholar 

  5. K.L. Chung and R.J. Williams. Introduction to Stochastic Integration. Birkhäuser Verlag, Basel, Boston, Berlin, 1983.

    MATH  Google Scholar 

  6. J.L. Doob. Stochastic Processes. John Wiley & Sons, New York, London, Sydney, 1967.

    Google Scholar 

  7. N. Dunford and J.T. Schwartz. Linear Operators, Part I. Interscience Publishers, New York, 1958.

    Google Scholar 

  8. A. Grothendieck. Resumé de la théorie metrique des produits tensoriels topologique. Bol. Soc. Matem. Saõ Paulo, 8,1956.

    Google Scholar 

  9. K. Itô. Stochastic integral. Proc. Imp. Acad. Tokyo, 20:519–524,1944.

    Article  MathSciNet  MATH  Google Scholar 

  10. K. Itô. Stochastic differential equations. Mem. Am. Math Soc., 4,1951.

    Google Scholar 

  11. J.-P. Kahane. Some Random Series of Functions. Cambridge University Press, Cambridge, U.K., second edition, 1985.

    MATH  Google Scholar 

  12. P.E. Kopp. Martingales and Stochastic Integrals. Cambridge University Press, Cambridge, U.K., 1984.

    Book  MATH  Google Scholar 

  13. J. Lindenstrauss and A. Pelczynski. Absolutely summing operators in 004Cp-spaces and their applications. Studia Math., 29:275–326,1968.

    MathSciNet  MATH  Google Scholar 

  14. J.E. Littlewood. On bounded bilinear forms in an infinite number of variables. Quarterly J. of Math. Oxford, 1:164–174,1930.

    Article  Google Scholar 

  15. M. Métivier. Semimartingales-a Course on Stochastic Processes. Walter de Gruyter, New York, 1982.

    Book  MATH  Google Scholar 

  16. M. Morse and W. Transue. Functionals of bounded Fréchet variation. Canadian J. Math., 1:153–165,1949.

    Article  MathSciNet  MATH  Google Scholar 

  17. R.E.A.C. Paley, N. Wiener, and A. Zygmund. Notes on random functions.Math. Zeitschr, 37:647–668,1933.

    Article  Google Scholar 

  18. G. Pisier. Factorization of linear operators and geometry of Banach spaces. In CBMS Regional Conf. Ser. in Math, volume 60, Providence, RI, 1986. American Mathematical Society.

    Google Scholar 

  19. P. Protter. Stochastic Integration and Differential Equations-A new Approach. Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, Hong Kong, 1990.

    MATH  Google Scholar 

  20. W. Rudin. Trigonometric series with gaps. J. Math. Mech., 9:203–227, 1960.

    MathSciNet  MATH  Google Scholar 

  21. N. Wiener. Differential-space. J. Math and Physics, 2:131–174,1923.

    Google Scholar 

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© 1992 Springer Science+Business Media Dordrecht

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Blei, R.C. (1992). A basic view of stochastic integration. In: Byrnes, J.S., Byrnes, J.L., Hargreaves, K.A., Berry, K. (eds) Probabilistic and Stochastic Methods in Analysis, with Applications. NATO ASI Series, vol 372. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2791-2_32

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  • DOI: https://doi.org/10.1007/978-94-011-2791-2_32

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5239-9

  • Online ISBN: 978-94-011-2791-2

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