A REPRESENTATION FOR AN INVERSE GENERALIZED FOURIER-FEYNMAN TRANSFORM ASSOCIATED WITH GAUSSIAN PROCESS ON FUNCTION SPACE
A Representation for an Inverse Generalized Fourier-Feynman Transform associated with Gaussian Process on Function Space
한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2021, v.28 no.4, pp.281-296
https://doi.org/https://doi.org/10.7468/jksmeb.2021.28.4.281
Choi, Jae Gil
(School of General Education, Dankook University)
Choi, Jae Gil.
(2021). A REPRESENTATION FOR AN INVERSE GENERALIZED FOURIER-FEYNMAN TRANSFORM ASSOCIATED WITH GAUSSIAN PROCESS ON FUNCTION SPACE. 한국수학교육학회지시리즈B:순수및응용수학, 28(4), 281-296, https://doi.org/https://doi.org/10.7468/jksmeb.2021.28.4.281
Abstract
In this paper, we suggest a representation for an inverse transform of the generalized Fourier-Feynman transform on the function space C<sub>a,b</sub>[0, T]. The function space C<sub>a,b</sub>[0, T] is induced by the generalized Brownian motion process with mean function a(t) and variance function b(t). To do this, we study the generalized Fourier-Feynman transform associated with the Gaussian process Ƶ<sub>k</sub> of exponential-type functionals. We then establish that a composition of the Ƶ<sub>k</sub>-generalized Fourier-Feynman transforms acts like an inverse generalized Fourier-Feynman transform.
- keywords
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generalized Fourier-Feynman transform,
generalized Brownian motion process,
Gaussian process,
exponential-type functional,
inverse transform