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Stochastic integration in hyperfinite dimensional linear spaces

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Nonstandard Analysis-Recent Developments

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 983))

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References

  1. R.M. Anderson: A Nonstandard Representation of Brownian Motion and Itô Integration. Israel J. Math. 25 (1976) pp. 15–46.

    Article  MathSciNet  MATH  Google Scholar 

  2. R.M. Anderson: Star-finite Probability Theory. Ph.D.-thesis, Yale University, 1977.

    Google Scholar 

  3. A. Bensoussan and R. Teman: Equation aux Derivées Partielles Stochastiques, Israel J. Math. 11 (1972)

    Google Scholar 

  4. A. Chojnowska-Michalik: Stochastic Differential Equations in Hilbert Spaces, in Z. Ciesielski (ed): Probability Theory. Banach Center Publications, Vol. 5, PWN, 1979.

    Google Scholar 

  5. P.-L. Chow: Stochastic Partial Differential Equations in Turbulence Related Problems, in A.T. Bharucha-Reid (ed): Probabilistic Analysis and Related Topics 1, Academic Press 1978

    Google Scholar 

  6. L. Gross: Abstract Wiener Spaces, Proc. 5th. Berkeley Sym. Math. Stat. Prob. 2 (1965), pp 31–42.

    Google Scholar 

  7. H.J. Keisler: An Infinitesimal Approach to Stochastic Analysis, Preliminary Version, 1978. (To app. Mem. AMS)

    Google Scholar 

  8. H.-H. Kuo: Gaussian Measures in Banach Spaces, LNM 463, Springer-Verlag, 1975.

    Google Scholar 

  9. T.L. Lindstrøm: Hyperfinite Stochastic Integration I: The Nonstandard Theory. Math. Scand. 46, pp265–292.

    Google Scholar 

  10. T.L. Lindstrøm: Hyperfinite Stochastic Integration II: Comparison with the Standard Theory. Math. Scand. 46, pp293–324.

    Google Scholar 

  11. T.L. Lindstrøm: Hyperfinite Stochastic Integration III: Hyperfinite Representations of Standard Martingales. Math. Scand. 46 (1980), pp 315–332.

    MathSciNet  MATH  Google Scholar 

  12. T.L. Lindstrøm: A Loeb-measure Approach to Theorems by Prohorov, Sazonov, and Gross. Trans AMS 269 (1982).

    Google Scholar 

  13. P.A. Loeb: An Introduction to Nonstandard Analysis and Hyperfinite Probability Theory, in A.T. Bharucha-Reid (ed): Probabilistic Analysis and Related Topics 2, Academic Press, 1979, pp 105–142.

    Google Scholar 

  14. E. Pardoux: Equations aux derivées partielles stochastiques monotones, C.R. Acad. Sci. Paris, Ser. A, 275(1972).

    Google Scholar 

  15. M. Reed and B. Simon: Methods of Modern Mathematical Physics II, Academic Press, 1975.

    Google Scholar 

  16. K.D. Stroyan and W.A.J. Luxemburg: Introduction to the Theory of Infinitesimals, Academic Press, 1976.

    Google Scholar 

  17. D.N. Hoover and E.A. Perkins: Nonstandard Construction of the Stochastic Integral and Applications to Stochastic Differential Equations, I–II, To appear Trans. AMS.

    Google Scholar 

  18. T.L. Lindstrøm: The Structure of Hyperfinite Stochastic Integrals. To appear Zeit. f. Wahr. Theorie.

    Google Scholar 

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Author notes

  1. Tom L. Lindstrøm

    Present address: Department of Mathematics, University of Wisconsin, 53706, Madison, Wisconsin

Authors and Affiliations

  1. University of Oslo, Norway

    Tom L. Lindstrøm

Authors
  1. Tom L. Lindstrøm
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Albert Emerson Hurd

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© 1983 Springer-Verlag

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Lindstrøm, T.L. (1983). Stochastic integration in hyperfinite dimensional linear spaces. In: Hurd, A.E. (eds) Nonstandard Analysis-Recent Developments. Lecture Notes in Mathematics, vol 983. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0065338

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  • DOI: https://doi.org/10.1007/BFb0065338

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12279-1

  • Online ISBN: 978-3-540-39602-4

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