Abstract
We establish a change of path formula for generalized Wiener integrals and develop a rotation theorem for Wiener measure with respect to Gaussian paths.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bearman J. E.: Rotations in the product of two Wiener spaces, Proc. Amer. Math. Soc. 3, 129–137 (1952)
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.
R. H. Cameron and D. A. Storvick, An operator valued Yeh-Wiener integral, and a Wiener integral equation, Indiana Univ. Math. J. 25 (1976), 235–258.
R. H. Cameron and D. A. Storvick, Relationships between the Wiener integral and the analytic Feynman integral. Rend. Circ. Mat. Palermo (2) Suppl. 17 (1987), 117–133.
R. H. Cameron and D. A. Storvick, Change of scale formulas for Wiener integral, Rend. Circ. Mat. Palermo (2) Suppl. 17 (1987), 105–115.
D. M. Chung, Scale-invariant measurability in abstract Wiener spaces, Pacific J. Math. 130 (1987), 27–40.
D. M. Chung, C. Park, and D. Skoug, Generalized Feynman integrals via conditional Feynman integrals, Michigan Math. J. 40 (1993), 377–391.
T. Huffman, C. Park, and D. Skoug, Convolutions and Fourier–Feynman transforms of functionals involving multiple integrals, Michigan Math. J. 43 (1996), 247–261.
T. Huffman, C. Park, and D. Skoug, Convolution and Fourier–Feynman transforms, Rocky Mountain J. Math. 27 (1997), 827–841.
G. W. Johnson and D. L. Skoug, Scale-invariant measurability in Wiener space, Pacific J. Math. 83 (1979), 157–176.
Y. S. Kim, A change of scale formula for Wiener integrals of cylinder functions on abstract Wiener space, Int. J. Math. Math. Sci. 21 (1998), 73–78.
R. E. A. C. Paley, N. Wiener, and A. Zygmund, Notes on random functions, Math. Z. 37 (1933), 647–668.
C. Park and D. Skoug, A note on Paley–Wiener–Zygmund stochastic integrals, Proc. Amer. Math. Soc. 103 (1988), 591–601.
C. Park and D. Skoug, A Kac-Feynman integral equation for conditional Wiener integrals, J. Integral Equations Appl. 3 (1991), 411–427.
C. Park and D. Skoug, Generalized Feynman integrals: The \({\mathcal L(L_2,L_2)}\) theory, Rocky Mountain J. Math. 25 (1995), 739–756.
C. Park and D. Skoug, Conditional Fourier–Feynman transforms and conditional convolution products, J. Korean Math. Soc. 38 (2001), 61–76.
D. Skoug and D. Storvick, A survey of results involving transforms and convolutions in function space, Rocky Mountain J. Math 34 (2004), 1147–1175.
I. Yoo and D. Skoug, A change of scale formula for Wiener integrals on abstract Wiener spaces, Int. J. Math. Math. Sci. 17 (1994), 239–248.
I. Yoo, T. S. Song, B. S. Kim, and K. S. Chang, A change of scale formula for Wiener integrals of unbounded functions, Rocky Mount. J. Math. 34 (2004), 371–389.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Choi, J.G., Chang, S.J. Note on generalized Wiener integrals. Arch. Math. 101, 569–579 (2013). https://doi.org/10.1007/s00013-013-0595-z
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00013-013-0595-z