JOURNAL BROWSE
Search
Advanced SearchSearch Tips
THE GENERALIZED ANALOGUE OF WIENER MEASURE SPACE AND ITS PROPERTIES
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Honam Mathematical Journal
  • Volume 32, Issue 4,  2010, pp.633-642
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2010.32.4.633
 Title & Authors
THE GENERALIZED ANALOGUE OF WIENER MEASURE SPACE AND ITS PROPERTIES
Ryu, Kun-Sik;
  PDF(new window)
 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].
 Keywords
generalized analogue of Wiener measure space;Fernique theorem;scale-invariant measurable subset;
 Language
English
 Cited by
1.
THE TRANSLATION THEOREM ON THE GENERALIZED ANALOGUE OF WIENER SPACE AND ITS APPLICATIONS,;

충청수학회지, 2013. vol.26. 4, pp.735-742 crossref(new window)
1.
THE TRANSLATION THEOREM ON THE GENERALIZED ANALOGUE OF WIENER SPACE AND ITS APPLICATIONS, Journal of the Chungcheng Mathematical Society, 2013, 26, 4, 735  crossref(new windwow)
 References
1.
G. W. Johnson and D. L. Skoug, Scale-invariant measurability in Wiener space, Pacific J. Math., 83(1979), pp. 157-176. crossref(new window)

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. crossref(new window)

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.