L2-sequential transforms on function space

A Representation for the Inverse Generalised Fourier–feynman Transform via Convolution Product on Function Space

“…In [5], Chang and Skoug defined a generalised analytic Fourier-Feynman transform (GFFT) for functionals on the very general function space C a,b [0, T ]. The function space C a,b [0, T ], induced by a generalised Brownian motion process (GBMP), was introduced by Yeh [13,14] and used extensively in [3][4][5][6][7].…”

“…The representation for an inverse transform of the 'analytic' GFFT has been studied [4,6,7], but the inverse transform of the GFFT investigated in [4,6,7] is not an analytic transform. In this paper, we study other representations for the inverse transform of the analytic GFFT on the function space C a,b [0, T ].…”

Effect of drift of the generalized Brownian motion process: an example for the analytic Feynman integral

“…The function space C a,b [0, T ], induced by a GBMP, was introduced by Yeh in [30], and was used extensively in [4,8,[10][11][12][13]20]. There have also been several attempts to construct financial mathematical theories using this process, see [18,21,25].…”

“…In this note, we set c = a(0) = b(0) = 0. Then the function space C a,b [0, T ] induced by the GBMP Y determined by the a(·) and b(·) can be considered as the space of continuous sample paths of Y , see [4][5][6][7][8][9][10][11][12][13][14][15][16]20], and one can see that for each t ∈ [0, T ],…”

“…However, the stochastic process used in this paper, as well as in [4][5][6][7][8][9][10][11][12][13][14][15][16]18,20,21,25,30], is non-stationary in time and is subject to a drift because In this note, we present an example of a bounded functional which is not generalized analytic Feynman integrable on the function space C a,b [0, T ].…”