Honam Mathematical Journal (호남수학학술지)

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THE GENERALIZED ANALOGUE OF WIENER MEASURE SPACE AND ITS PROPERTIES

  • Ryu, Kun-Sik (Department of Mathematics Education Han Nam University)
  • Received : 2010.10.07
  • Accepted : 2010.11.15
  • Published : 2010.12.25
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Abstract

In this note, we introduce the definition of the generalized analogue of Wiener measure on the space C[a, b] of all real-valued continuous functions on the closed interval [a, b], give several examples of it and investigate some important properties of it - the Fernique theorem and the existence theorem of scale-invariant measurable subsets on C[a, b].

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References

  1. G. W. Johnson and D. L. Skoug, Scale-invariant measurability in Wiener space, Pacific J. Math., 83(1979), pp. 157-176. https://doi.org/10.2140/pjm.1979.83.157
  2. G. W. Johnson and M. L. Lapidus, The Feynman integral and Feynman's operational calculus, Oxford Mathematical Monographs, Oxford Univ. Press, (2000).
  3. K. S. Ryu and M. K. Im, A measure-valued analogue of Wiener measure and the measure-valued Feynman-Kac formnula, Trans. Amer. Math. Soc., 354(2002), pp. 4921-4951. https://doi.org/10.1090/S0002-9947-02-03077-5
  4. M. X. Fernique, Integrabilite des Vecteurs Gaussians, Academie des Sciences, Paris Comptes Rendus, 270(1970), pp. 1698-1699.
  5. A. V. Skorokhod, Notes on Gaussian measure in a Banach space, Toer. Veroj. I Prim., 15(1970), pp. 517-520.
  6. K. R. Parthasarathy, Probability measures on metric spaces, Academic Press, New York, 1967.
  7. K. S. Ryu, The generalized Fernique's theorem for analogue of Wiener measure space, J. Chungcheong Math. Soc., 22(2009), 743-748.
  8. H. G. Tucker, A groduate course in probability, Academic press, New York (1967).
  9. N. Wiener, Differential space, J. Math. Phys., 2(1923), pp. 131-174. https://doi.org/10.1002/sapm192321131

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