Conditional integral transforms and convolutions for a general vector-valued conditioning functions
2
조회
0
다운로드
1
인용
0
참고문헌
키워드
초록
We study the conditional integral transforms and conditional convolutions of functionals defined on $K[0, T]$. We consider a general vector-valued conditioning functions $X_k (x) = \left(\gamma_1 (x), \ldots, \gamma_k (x)\right)$ where $\gamma_j (x)$ are Gaussian random variables on the Wiener space which need not depend upon the values of $x$ at only finitely many points in $(0, T]$. We then obtain several relationships and formulas for the conditioning functions that exist among conditional integral transform, conditional convolution and first variation of functionals in $E_\sigma$.
Abstract
We study the conditional integral transforms and conditional convolutions of functionals defined on $K[0, T]$. We consider a general vector-valued conditioning functions $X_k (x) = \left(\gamma_1 (x), \ldots, \gamma_k (x)\right)$ where $\gamma_j (x)$ are Gaussian random variables on the Wiener space which need not depend upon the values of $x$ at only finitely many points in $(0, T]$. We then obtain several relationships and formulas for the conditioning functions that exist among conditional integral transform, conditional convolution and first variation of functionals in $E_\sigma$.
참고문헌 (14)
- R.H.Cameron, "The first variation of an indefinite Wiener integral", Proc. Amer. Math. Soc, 2 (1951)
- R.H.Cameron, "Fourier-Wiener transforms of analytic functionals", Duke Math. J, 12, pp.489~507 (1945)
- R.H.Cameron, "An L2 analytic Fourier-Feynman transform", Michigan Math. J, 23, pp.1~30 (1976)
- D.M.Chung, "Conditional analytic Feynman integrals and a related Schrodinger integral equation", Siam. J. Math. Anal, 20, pp.950~965 (1989)
- B.A.Fuks, "Theory of analytic functions of several complex variables" (1963), Amer. Math. Soc
- 김봉진, "Generalized conditional integral transforms, conditional convolutions and first variations", 한국수학논문집, 20(1), pp.1~18 (2012), 강원경기수학회
- B.J.Kim, "Integral transforms, convolution products and rst variations", Internat. J. Math. Math. Sci, 2004(11), pp.579~598 (2004)
- B.J.Kim, "Conditional integral transforms, conditional convolution products and first variations", PanAmerican Math. J, 14, pp.27~47 (2004)
- Y.J.Lee, "Integral transforms of analytic functions on abstract Wiener spaces", J. Funct. Anal, 47, pp.153~164 (1982)
- I.Y.Lee, "Integration formulas for the conditional transform involving the first variation", Bull.Iranian Math. Soc, 41, pp.771~783 (2015)
- C.Park, "Conditional Fourier-Feynman transforms and conditional convolution products", J. Korean Math. Soc, 38, pp.61~76 (2001)
- C.Park, "A simple formula for conditional Wiener integrals with applications", Pacific J. Math, 135, pp.381~394 (1988)
- C.Park, "Conditional Wiener integrals II", Pacific J. Math, 167, pp.293~312 (1995)
- D.Skoug, "A survey of results involving transforms and convolutions in function space", Rocky Mountain J. Math, 34, pp.1147~1175 (2004)