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TRANSFORM ON GAUSSIAN WHITE NOISE FUNCTIONALS AND FEYNMAN INTEGRAL
Un Cig Ji, Young Yi Kim 충북대학교 금융수학연구소 2013 금융수학연구소학술지 Vol.8 No.-
We develop Gaussian white noise functionals with mean functional and covariance operator, and study transforms on the Gaussian white noise functionals. The innitesimal generators of all dierentiable one-parameter groups induced by the transforms are linear combinations of the Gross Laplacian and the number op- erator. Finally we study Feynman integrals of the Gaussian white noise functionals, and some relations between the transforms and the Feynman integrals.
STOCHASTIC DIFFERENTIAL EQUATION FOR WHITE NOISE FUNCTIONALS
Un Cig Ji 충청수학회 2016 충청수학회지 Vol.29 No.2
Within white noise approach, we study the existence and uniqueness of the solution of an initial value problem for generalized white noise functionals, and then as a corollary we discuss the linear stochastic differential equation associated with a convolution of white noise functionals.
INFINITESIMAL GENERATORS OF THE GENERALIZED FOURIER{GAUSS TRANSFORMS
Un Cig Ji,Young Yi Kim 충청수학회 2010 충청수학회지 Vol.23 No.1
In this note, we investigate the innitesimal generators of the transformation groups induced by the Fourier{Gauss and Fourier{Mehler transforms on white noise functionals.