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CHANGE OF SCALE FORMULAS FOR CONDITIONAL WIENER INTEGRALS AS INTEGRAL TRANSFORMS OVER WIENER PATHS IN ABSTRACT WIENER SPACE
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 Title & Authors
CHANGE OF SCALE FORMULAS FOR CONDITIONAL WIENER INTEGRALS AS INTEGRAL TRANSFORMS OVER WIENER PATHS IN ABSTRACT WIENER SPACE
Cho, Dong-Hyun;
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 Abstract
In this paper, we derive a change of scale formula for conditional Wiener integrals, as integral transforms, of possibly unbounded functions over Wiener paths in abstract Wiener space. In fact, we derive the change of scale formula for the product of the functions in a Banach algebra which is equivalent to both the Fresnel class and the space of measures of bounded variation over a real separable Hilbert space, and the cylinder functions over Wiener paths in abstract Wiener space. As an application of the result, we obtain a change of scale formula for the conditional analytic Fourier-Feynman transform of the product of the functions.
 Keywords
change of scale formula;conditional analytic Feynman integral;conditional analytic Fourier-Feynman transform;conditional analytic Wiener integral;conditional Wiener integral;
 Language
English
 Cited by
1.
GENERALIZED ANALYTIC FEYNMAN INTEGRAL VIA FUNCTION SPACE INTEGRAL OF BOUNDED CYLINDER FUNCTIONALS,;;;

대한수학회보, 2011. vol.48. 3, pp.475-489 crossref(new window)
1.
SCALE TRANSFORMATIONS FOR PRESENT POSITION-INDEPENDENT CONDITIONAL EXPECTATIONS, Journal of the Korean Mathematical Society, 2016, 53, 3, 709  crossref(new windwow)
2.
Integral Transforms on a Function Space with Change of Scales Using Multivariate Normal Distributions, Journal of Function Spaces, 2016, 2016, 1  crossref(new windwow)
 References
1.
R. H. Cameron, The translation pathology of Wiener space, Duke Math. J. 21 (1954), 623-628 crossref(new window)

2.
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 crossref(new window)

3.
R. H. Cameron and D. A. Storvick, Relationships between the Wiener integral and the analytic Feynman integral, Supplimento ai Rendiconti del Circolo Matematico di Palermo, Serie II-Numero 17 (1987), 117-133

4.
R. H. Cameron and D. A. Storvick, Change of scale formulas for Wiener integral, Supplimento ai Rendiconti del Circolo Matematico di Palermo, Serie II-Numero 17 (1987), 105-115

5.
K. S. Chang, D. H. Cho, and I. Yoo, A conditional analytic Feynman integral over Wiener paths in abstract Wiener space, Intern. Math. J. 2 (2002), no. 9, 855-870

6.
K. S. Chang, G. W. Johnson, and D. L. Skoug, Functions in the Fresnel class, Proc. Amer. Math. Soc. 100 (1987), 309-318 crossref(new window)

7.
K. S. Chang, B. S. Kim, T. S. Song, and I. Yoo, A change of scale formula for Wiener integrals of unbounded functions, Rocky Mount. J. Math. 34 (2004), no. 1, 371-389 crossref(new window)

8.
D. H. Cho, Conditional analytic Feynman integral over product space of Wiener paths in abstract Wiener space, to appear in Rocky Mount. J. Math

9.
G. Kallianpur and C. Bromley, Generalized Feynman integrals using analytic continuation in several complex variables, Stochastic Analysis and Applications, Dekker, 1984

10.
J. Kuelbs and R. LePage, The law of the iterated logarithm for Brownian motion in a Banach space, Trans. Amer. Math. Soc. 185 (1973), 253-264 crossref(new window)

11.
H. H. Kuo, Gaussian measures in Banach spaces, Lecture Notes in Mathematics 463, Springer-Verlag, 1975

12.
K. S. Ryu, The Wiener integral over paths in abstract Wiener space, J. Korean Math. Soc. 29 (1992), no. 2, 317-331

13.
I. Yoo and D. L. Skoug, A change of scale formula for Wiener integrals on abstract Wiener spaces, Internat. J. Math. Math. Sci. 17 (1994), 239-248 crossref(new window)

14.
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), no. 1, 115-129

15.
I. Yoo and G. J. Yoon, Change of scale formulas for Yeh-Wiener integrals, Commun. Korean Math. Soc. 6 (1991), no. 1, 19-26