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http://dx.doi.org/10.14403/jcms.2011.24.3.11

A CHANGE OF SCALE FORMULA FOR ENERALIZED WIENER INTEGRALS  

Kim, Byoung Soo (School of Liberal Arts Seoul National University of Science and Technology)
Song, Teuk Seob (Department of Computer Engineering Mokwon University)
Yoo, Il (Department of Mathematics Yonsei University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.24, no.3, 2011 , pp. 517-528 More about this Journal
Abstract
Cameron and Storvick introduced change of scale formulas for Wiener integrals of bounded functions in the Banach algebra $\mathcal{S}$ of analytic Feynman integrable functions on classical Wiener space. Yoo and Skoug extended this result to an abstract Wiener space. Also Yoo, Song, Kim and Chang established a change of scale formula for Wiener integrals of functions on abstract Wiener space which need not be bounded or continuous. In this paper, we investigate a change of scale formula for generalized Wiener integrals of various functions on classical Wiener space.
Keywords
change of scale formula; Wiener integral; generalized Wiener integral; generalized Feynman integral;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
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1 R. H. Cameron and W. T. Martin, The behavior of measure and measurability under change of scale in Wiener space, Bull. Amer. Math. Soc. 53 (1947), 130-137.   DOI
2 R.H. Cameron and D.A. Storvick, Some Banach algebras of analytic Feynman integrable functionals, in Analytic functions, Kozubnik Lecture Notes in Math. 798 (1980), 18-27.
3 R.H. Cameron and D.A. Storvick, Change of scale formulas for Wiener integral, Supplemento ai Rendiconti del Circolo Matematico di Palermo, Serie II-Numero, 17 (1987), 105-115.
4 R.H. Cameron and D.A. Storvick, Relationships between the Wiener integral and the analytic Feynman integral, Supplemento ai Rendiconti del Circolo Matematico di Palermo, Serie II-Numero, 17 (1987), 117-133.
5 R.H. Cameron and D.A. Storvick, New existence theorems and evaluation formulas for analytic Feynman integrals, Deformations of Mathematics Structures, 297-308, Kluwer, Dordrecht, 1989.
6 D.M. Chung, C. Park and D. Skoug, Generalized Feynman integrals via conditional Feynman integrals, Michigan Math. J., 40 (1993), 377-391.   DOI
7 G. W. Johnson and D. L. Skoug, Scale-invariant measurability in Wiener space, Pacific J. Math. 83 (1979), 157-176.   DOI
8 G. W. Johnson and D. L. Skoug, Stability theorems for the Feynman integral, Supplemento ai Rendiconti del Circolo Matematico di Palermo, Serie II-Numero, 8 (1985), 361-367.
9 T. Huffman, C. Park and D. Skoug, Analytic Fourier-Feynman transforms and convolution, Trans. Amer. Math. Soc. 347 (1995), 661-673.   DOI   ScienceOn
10 T. Huffman, C. Park and D. Skoug, Generalized transforms and convolutions, Internat. J. Math, & Math. Sci. 20 (1997), 19-32.   DOI   ScienceOn
11 I. Yoo, K. S. Chang, D. H. Cho, B. S. Kim and T. S. Song , A change of scale formula for conditional Wiener integrals on classical Wiener space, J. Korean Math. Soc. 44 (2007), 1025-1050.   DOI   ScienceOn
12 I. Yoo and D. L. Skoug, A change of scale formula for Wiener integrals on abstract Wiener spaces, International J. Math. and Math. Sci. 17 (1994), 239- 248.   DOI   ScienceOn
13 I. Yoo and D. L. Skoug, A change of scale formula for Wiener integrals on abstract Wiener spaces II, J. Korean Math. Soc. 31 (1994), 115-129.
14 I. Yoo, T. S. Song, B. S. Kim and K.S. Chang, A change of scale formula for Wiener integrals of unbounded functions, Rocky Mountain J. Math. 34(2004), 371-389.   DOI   ScienceOn
15 I. Yoo and G. J. Yoon, Change of scale formulas for Yeh-Wiener integrals, Comm. Korean Math. Soc. 6 (1991), 19-26.