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On Fourier transform of generalized Brownian functionals. (English) Zbl 0491.60039


MSC:

60G20 Generalized stochastic processes
60J65 Brownian motion
42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
46F25 Distributions on infinite-dimensional spaces
60G15 Gaussian processes
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
42C99 Nontrigonometric harmonic analysis

Citations:

Zbl 0432.60002
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Full Text: DOI

References:

[1] Gel’fand, I. M.; Vilenkin, N. Ya, Generalized functions, (Applications of Harmonic Analysis, Vol. 4 (1964), Academic Press) · Zbl 0136.11201
[2] Hida, T., (Analysis of Brownian Functionals (1975), Carleton University: Carleton University Ottawa), Carleton Math. Lecture Notes, No. 13 · Zbl 1089.60522
[3] Hida, T., Generalized multiple Wiener integrals, (Proc. Japan Acad. Ser. A Math. Sci., 54 (1978)), 55-58 · Zbl 0389.60026
[4] Hida, T., (Brownian Motion, Application of Math., Vol. 11 (1980), Springer-Verlag: Springer-Verlag Heidelberg/Berlin/New York) · Zbl 0432.60002
[5] Hida, T., The role of exponential functions in the analysis of generalized Brownian functionals (1981), Preprint · Zbl 0495.60047
[6] Kubo, I.; Takenaka, S., Calculus on Gaussian white noise I, (Proc. Japan Acad. Ser. A Math. Sci., 56 (1980)), 376-380 · Zbl 0459.60068
[7] Kubo, I.; Takenaka, S., Calculus on Gaussian white noise II, (Proc. Japan Acad. Ser. A Math. Sci., 56 (1980)), 411-416 · Zbl 0475.60064
[8] Kuo, H.-H, Integration by parts for abstract Wiener measures, Duke Math. J., 41, 373-379 (1974) · Zbl 0312.28012
[9] Kuo, H.-H, Fourier-Wiener transform on Brownian functionals, (Lecture Notes in Math. No. 828 (1980), Springer-Verlag: Springer-Verlag Heidelberg/Berlin/New York), 146-161 · Zbl 0445.60064
[10] Streit, L.; Hida, T., Generalized Brownian functionals and Feynman integral (1981), Preprint · Zbl 0575.60039
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