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Stochastic integral equations and diffusions on Banach spaces

Part of the Lecture Notes in Mathematics book series (LNM,volume 1080)

Keywords

  • Banach Space
  • Markov Process
  • Cauchy Sequence
  • Predictable Process
  • Gaussian Random Field

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References

  1. A. ARAUJO, E. GINE: The central limit theorem for real and Banach valued random variables. New York-Chichester-Brisbane-Toronto: Wiley 1980.

    MATH  Google Scholar 

  2. E. DETTWEILER: Grenzwertsätze für Wahrscheinlichkeitsmaße auf Badrikianschen Räumen. Z. Wahrscheinlichkeitstheorie verw. Gebiete 34, 285–311 (1976).

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. E. DETTWEILER: Poisson measures on Banach lattices. In: Probability measures on groups. Proceedings of the 6th conference in Oberwolfach, Ed. H. Heyer. Lecture Notes in Math. 928, 16–45. Berlin-Heidelberg-New York: Springer 1983.

    CrossRef  Google Scholar 

  4. E. DETTWEILER: Banach space valued processes with independent increments and stochastic integration. In: Probability in Banach spaces IV, Proceedings, Oberwolfach 1982, Eds A. Beck and K. Jacobs. Lecture Notes in Math. 990, 54–83. Berlin-Heidelberg-New York: Springer 1983.

    Google Scholar 

  5. E.B. DYNKIN: Die Grundlagen der Theorie der Markoffschen Prozesse. Berlin-Göttingen-Heidelberg: Springer 1961.

    CrossRef  MATH  Google Scholar 

  6. E.B. DYNKIN: Markov processes, volume I & II. Berlin-Göttingen-Heidelberg: Springer 1965.

    CrossRef  MATH  Google Scholar 

  7. I.I. GIHMAN, A.V. SKOROHOD: The theory of stochastic processes I, II, III. Berlin-Heidelberg-New York: Springer 1974 (vol.I), 1975 (vol.II), 1979 (vol.III).

    CrossRef  MATH  Google Scholar 

  8. I.I. GIHMAN, A.V. SKOROHOD: Introduction to the theory of random processes. Philadelphia-London-Toronto: Saunders 1969.

    MATH  Google Scholar 

  9. J. HOFFMANN-JØRGENSEN, G. PISIER: The law of large numbers and the central limit theorem in Banach spaces. Ann. Prob. 4, 587–599 (1976).

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. H.-H. KUO: Stochastic integrals in abstract Wiener space. Pacific Journal of Math. 41, 469–483 (1972).

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. M. METIVIER: Semimartingales. Berlin-New York: de Gruyter 1982

    CrossRef  MATH  Google Scholar 

  12. G. PISIER: Martingales with values in uniformly convex spaces. Israel J. Math. 20, 326–350 (1975).

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. J. ROSINSKI: Central limit theorems for dependent random vectors in Banach spaces. In: Martingale theory in harmonic analysis and Banach spaces, Proceedings, Cleveland 1981, Eds J.-A. Chao and W.A. Woyczynski. Lecture Notes in Math. 939. Berlin-Heidelberg-New York: Springer 1982.

    Google Scholar 

  14. D.W. STROOCK, S.R.S. VARADHAN: Multidimensional diffusion processes. Berlin-Heidelberg-New York: Springer 1979.

    MATH  Google Scholar 

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© 1984 Springer-Verlag

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Dettweiler, E. (1984). Stochastic integral equations and diffusions on Banach spaces. In: Szynal, D., Weron, A. (eds) Probability Theory on Vector Spaces III. Lecture Notes in Mathematics, vol 1080. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099783

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  • DOI: https://doi.org/10.1007/BFb0099783

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13388-9

  • Online ISBN: 978-3-540-38939-2

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