TY - JOUR
A2 - Rodríguez-Dagnino, Ramón M.
AU - Cho, Dong Hyun
PY - 2017
DA - 2017/02/28
TI - A Conditional Fourier-Feynman Transform and Conditional Convolution Product with Change of Scales on a Function Space II
SP - 8510782
VL - 2017
AB - Using a simple formula for conditional expectations over continuous paths, we will evaluate conditional expectations which are types of analytic conditional Fourier-Feynman transforms and conditional convolution products of generalized cylinder functions and the functions in a Banach algebra which is the space of generalized Fourier transforms of the measures on the Borel class of L2[0,T]. We will then investigate their relationships. Particularly, we prove that the conditional transform of the conditional convolution product can be expressed by the product of the conditional transforms of each function. Finally we will establish change of scale formulas for the conditional transforms and the conditional convolution products. In these evaluation formulas and change of scale formulas, we use multivariate normal distributions so that the conditioning function does not contain present positions of the paths.
SN - 1687-952X
UR - https://doi.org/10.1155/2017/8510782
DO - 10.1155/2017/8510782
JF - Journal of Probability and Statistics
PB - Hindawi
KW -
ER -