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http://dx.doi.org/10.4134/CKMS.2007.22.1.091

CHANGE OF SCALE FORMULAS FOR CONDITIONAL WIENER INTEGRALS AS INTEGRAL TRANSFORMS OVER WIENER PATHS IN ABSTRACT WIENER SPACE  

Cho, Dong-Hyun (Department of Mathematics Kyonggi University)
Publication Information
Communications of the Korean Mathematical Society / v.22, no.1, 2007 , pp. 91-109 More about this Journal
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 $L_p-type$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;
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  • Reference
1 G. Kallianpur and C. Bromley, Generalized Feynman integrals using analytic continuation in several complex variables, Stochastic Analysis and Applications, Dekker, 1984
2 R. H. Cameron, The translation pathology of Wiener space, Duke Math. J. 21 (1954), 623-628   DOI
3 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
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   DOI   ScienceOn
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   DOI   ScienceOn
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 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   DOI   ScienceOn
10 H. H. Kuo, Gaussian measures in Banach spaces, Lecture Notes in Mathematics 463, Springer-Verlag, 1975
11 K. S. Ryu, The Wiener integral over paths in abstract Wiener space, J. Korean Math. Soc. 29 (1992), no. 2, 317-331
12 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   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), no. 1, 115-129
14 I. Yoo and G. J. Yoon, Change of scale formulas for Yeh-Wiener integrals, Commun. Korean Math. Soc. 6 (1991), no. 1, 19-26
15 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